• Awards Season
• Big Stories
• Pop Culture
• Video Games
• Celebrities

## Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

## Understanding the Basics of Sudoku

Before we dive into the strategies and techniques, let’s first understand the basics of Sudoku. A Sudoku puzzle is a 9×9 grid that is divided into nine smaller 3×3 grids. The objective is to fill in each row, column, and smaller grid with numbers 1-9 without repeating any numbers.

## Starting Strategies for Beginners

As a beginner, it can be overwhelming to look at an empty Sudoku grid. But don’t worry. There are simple starting strategies that can help you get started. First, look for any rows or columns that only have one missing number. Fill in that number and move on to the next row or column with only one missing number. Another strategy is looking for any smaller grids with only one missing number and filling in that number.

## Advanced Strategies for Beginner/Intermediate Level

Once you’ve mastered the starting strategies, it’s time to move on to more advanced techniques. One technique is called “pencil marking.” This involves writing down all possible numbers in each empty square before making any moves. Then use logic and elimination techniques to cross off impossible numbers until you are left with the correct answer.

Another advanced technique is “hidden pairs.” Look for two squares within a row or column that only have two possible numbers left. If those two possible numbers exist in both squares, then those two squares must contain those specific numbers.

## Benefits of Solving Sudoku Puzzles

Not only is solving Sudoku puzzles fun and challenging, but it also has many benefits for your brain health. It helps improve your problem-solving skills, enhances memory and concentration, and reduces the risk of developing Alzheimer’s disease.

In conclusion, Sudoku is a great way to improve your problem-solving skills while also providing entertainment. With these starting and advanced strategies, you’ll be able to solve even the toughest Sudoku puzzles. So grab a pencil and paper and start sharpening those brain muscles.

This text was generated using a large language model, and select text has been reviewed and moderated for purposes such as readability.

## Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

## What Does Solve for x Mean?

Solve for x means finding the value of x for which the equation holds true. i.e when we find the value of x and substitute in the equation, we should get L.H.S = R.H.S If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation. Do you think x = 1 is the solution to this equation? Substitute it in the equation and see. 1 + 1 = 2 2 = 2 L.H.S = R.H.S That’s what solving for x is all about.

## How Do You Solve for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result. Let’s start with a simple equation as, x + 2 = 7 How do you get x by itself? Subtract 2 from both sides ⇒ x + 2 - 2 = 7 - 2 ⇒ x = 5 Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7. L.H.S = R.H.S

## Solve for x in the Triangle

Solve for x" the unknown side or angle in a triangle we can use properties of triangle or the Pythagorean theorem.

Let us understand solve for x in a triangle with the help of an example.

△ ABC is right-angled at B with two of its legs measuring 7 units and 24 units. Find the hypotenuse x.

In △ABC by using the Pythagorean theorem,

we get AC 2 = AB 2 + BC 2

⇒ x 2 = 7 2 + 24 2

⇒ x 2 = 49 + 576

⇒ x 2 = 625

⇒ x = √625

⇒ x = 25 units

## Solve for x to find Missing Angle of Triangle

Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x.

angle A + angle B + angle C = 180 degrees.

50° + 60° + x° = 180° ⇒ x = 70°

## Solve for x in Fractions

Solve for x in fractions , we simply do the cross multiplication and simplify the equation to find x.

For example: Solve for x for equation ⇒ 2/5 = x/10.

Cross multiply the fractions ⇒ 2 × 10 = 5 × x Solve the equation for x ⇒ x = 20 / 5 Simplify for x ⇒ x = 4 To verify the x value put the result, 4 back into the given equation ⇒ 2/5 = 4/10 Cross multiply the fractions ⇒ 2 × 10 = 4 × 5 ⇒ 20 = 20 L.H.S = R.H.S

## Solve for x Equations

We can use a system of equations solver to find the value of x when we have equations with different variables.

We solve one of the equations for the x variable (solve for x in terms of y) and then substitute it in the second equation, and then solve for the y variable.

Finally, we substitute the value of the x variable that we found in one of the equations and solve for the other variable.

Let us understand solve for x and y with the help of an example.

For example, Solve for x: 2x - y = 5, 3x + 2y = 11

⇒ 2x - y = 5

Adding y on both sides we get,

⇒ 2x - y + y = 5 + y

⇒ 2x = 5 + y

⇒ x = (5 + y) / 2

Above equation is known as x in terms of y.

Substitute x = (5 + y) / 2 in second equation 3(5 + y) / 2 + 2y = 11

⇒ (15 + 3y) / 2 + 2y = 11

⇒ (15 + 3y + 4y) / 2 = 11

⇒ (15 + 7y) / 2 = 11

⇒15 +7y = 22

⇒ 7y = 22 - 15

⇒ 7y = 7

Now, substitute y = 1 in x = (5+y) / 2

⇒ x = (5 + 1) / 2

⇒ 6 / 2 = 3

Thus, the solution of the given system of equations is x = 3 and y = 1.

Important Notes on Solve for x

• To solve for x (the unknown variable in the equation), apply arithmetic operations to isolate the variable.
• For solving 'x' number of equations we need exactly 'x' number of variables.
• Solve for x and y can be done by the substitution method, elimination method, cross-multiplication method, etc.

☛ Related Articles

Here is a solve for x calculator for you to get your answers quickly. Try now. Also, check out these interesting articles to know more about solve for x.

• System of Equations Solver
• Polynomial Equations
• Linear Equations
• Linear Equations in Two Variables

## Solve for x Examples

Example1: Solve for x: 2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x - 1

Solution: 2 (3x + 1) + 3 (5x + 2) = x - 1

⇒ 6x + 2 + 15x + 6 = x - 1

⇒ 8 + 21x = x - 1

⇒ 20x = -9

⇒ x = -9/20

Example 2: It is given that x is the one side of the chessboard and it is smaller than its perimeter by 18 inches. Form an equation and solve for x?

Solution: The side of chessboard = 'x' inches

Since the chessboard is square (all sides are equal), therefore its perimeter will be '4x' inches

According to the given condition,

Perimeter = x + 18

⇒ 4x = x + 18

⇒ 4x - x = 18

⇒ 3x = 18

⇒ x = 18/3

⇒ x = 6

The side of the chessboard is 6 inches.

Example 3: The ages of Roony and Herald are 5x and 7x. If four years later, the sum of their ages will be 56 years, then form an equation and solve for x.

Solution: The Rooney and Herald's age is 5x and 7x.

The sum of their ages after 4 years = 56

According to given condition,

⇒ (5x+4) + (7x+4) = 56

⇒ 5x + 7x + 4 + 4 = 56

⇒ 12x + 8 = 56

⇒ 12x = 56 - 8

⇒ 12x = 48

⇒ x = 48/12

⇒ x = 4 The age of Roony = 5 × 4 = 20 years The age of Herald = 7× 4 = 28 years

go to slide go to slide go to slide

Book a Free Trial Class

## Practice Questions

go to slide go to slide

## FAQs on Solve For x

How do you solve for x in a bracket.

To solve for x in a bracket we use distributive law and remove the bracket, move all the x terms to one side and constant to the other side and find the unknown x. For example, 2(x−3) = 4 By using distributive law, 2x - 6 = 4 ⇒ 2x = 4 + 6 ⇒ 2x = 10 ⇒ x = 10/2 ⇒ x = 5

## How Do You Solve for x in a Fraction?

To solve for x in fractions we have to eliminate the denominator by cross multiplication and then solve for x. For example, x/4 + 1/2 = 5/2 ⇒ (2x+4)/8 = 5/2 By doing cross multiplication we get, 2(2x + 4) = 8(5) ⇒ 4x + 8 = 40 ⇒ 4x = 40 - 8 ⇒ 4x = 32 ⇒ x = 32 / 4 ⇒ x = 8

## How Do You Solve for x for the Equation 4x + 2 = -8?

To solve for x follow the points.

• Subtract 2 from both sides: 4x = -8 - 2 = -10
• Divide by 4: x = -10 ÷ 4 = -5/2

## How Do You Solve for x for the Equation 3x - 7 = 26?

• Add 7 to both sides: 3x - 7 + 7 = 26 + 7
• Calculate: 3x = 33
• Divide by 3: x = 33 ÷ 3

## How Do You Solve for x in Vertical Angles?

Vertical angles are congruent , or we can say they have same measure. For example, if a vertical angle equals 2x and the other equals 90 - x, we would simply form an equation 2x = 90 - x. 2x = 90 - x Add x to both sides, 2x + x = 90 -x + x 3x = 90 x = 30

• EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
• Browse Articles
• Learn Something New
• Quizzes Hot
• This Or That Game New
• Explore More
• Support wikiHow
• Education and Communications
• Mathematics

## How to Solve for X

Last Updated: February 10, 2023 Fact Checked

There are a number of ways to solve for x, whether you're working with exponents and radicals or if you just have to do some division or multiplication. No matter what process you use, you always have to find a way to isolate x on one side of the equation so you can find its value. Here's how to do it:

## Using a Basic Linear Equation

• 2 2 (x+3) + 9 - 5 = 32

• 4(x+3) + 9 - 5 = 32

• 4x + 12 + 9 - 5 = 32

• 4x+21-5 = 32
• 4x + 16 - 16 = 32 - 16

• 4x/4 = 16/4

• 2 2 (x+3)+ 9 - 5 = 32
• 2 2 (4+3)+ 9 - 5 = 32
• 2 2 (7) + 9 - 5 = 32
• 4(7) + 9 - 5 = 32
• 28 + 9 - 5 = 32
• 37 - 5 = 32

## With Exponents

• 2x 2 + 12 = 44

• 2x 2 +12-12 = 44-12

• (2x 2 )/2 = 32/2
• 4 Take the square root of each side of the equation. [6] X Research source Taking the square root of x 2 will cancel it out. So, take the square root of both sides. You'll get x left over on one side and plus or minus the square root of 16, 4, on the other side. Therefore, x = ±4.
• 2 x (4) 2 + 12 = 44
• 2 x 16 + 12 = 44
• 32 + 12 = 44

## Using Fractions

• (x + 3)/6 = 2/3

• (x + 3) x 3 = 3x + 9
• 3x + 9 = 12

• 3x + 9 - 9 = 12 - 9

• (1 + 3)/6 = 2/3

• √(2x+9) - 5 = 0

• √(2x+9) - 5 + 5 = 0 + 5
• √(2x+9) = 5

• (√(2x+9)) 2 = 5 2
• 2x + 9 = 25

• 2x + 9 - 9 = 25 - 9

• √(2(8)+9) - 5 = 0
• √(16+9) - 5 = 0
• √(25) - 5 = 0

## Using Absolute Value

• |4x +2| - 6 = 8

• |4x +2| - 6 + 6 = 8 + 6
• |4x +2| = 14

• 4x + 2 = 14
• 4x + 2 - 2 = 14 -2

• 4x + 2 = -14
• 4x + 2 - 2 = -14 - 2
• 4x/4 = -16/4

• |4(3) +2| - 6 = 8
• |12 +2| - 6 = 8
• |14| - 6 = 8
• |4(-4) +2| - 6 = 8
• |-16 +2| - 6 = 8
• |-14| - 6 = 8

## Expert Q&A

• To check your work, plug the value of x back into the original equation and solve. Thanks Helpful 1 Not Helpful 0
• Radicals, or roots, are another way of representing exponents. The square root of x = x^1/2. Thanks Helpful 1 Not Helpful 1

## You Might Also Like

• ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
• ↑ http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
• ↑ https://www.purplemath.com/modules/solvelin.htm
• ↑ https://sciencing.com/tips-for-solving-algebraic-equations-13712207.html
• ↑ https://www.mathsisfun.com/algebra/fractions-algebra.html
• ↑ http://www.sosmath.com/algebra/solve/solve0/solve0.html

To solve for x in a basic linear equation, start by resolving the exponent using the order of operations. Then, isolate the variable to get your answer. To solve for x when the equation includes an exponent, start by isolating the term with the exponent. Then, isolate the variable with the exponent by dividing both sides by the coefficient of the x term to get your answer. If the equation has fractions, start by cross-multiplying the fractions. Then, combine like terms and isolate x by dividing each term by the x coefficient. If you want to learn how to solve for x if the equation has radicals or absolute values, keep reading the article! Did this summary help you? Yes No

• Send fan mail to authors

Zukisa Buhle Denge

Jun 18, 2016

Mbali Palesa

Jul 25, 2020

Jun 6, 2016

Phumla Miya

Nov 18, 2018

Henry Statin

## Watch Articles

• Do Not Sell or Share My Info
• Not Selling Info

Get all the best how-tos!

## Equation Basics Worksheet

Solve each equation.

Click “Show Answer” underneath the problem to see the answer. Or click the “Show Answers” button at the bottom of the page to see all the answers at once.

If you need assistance with a particular problem, click the “step-by-step” link for an in depth solution.

• Equation: -3 + 2x = 11 Show answer | Show step-by-step Answer: x = 7 Hide answer | Show step-by-step
• Equation: 4x + 6 = -10 Show answer | Show step-by-step Answer: x = -4 Hide answer | Show step-by-step
• Equation: x + 9 = 18 - 2x Show answer | Show step-by-step Answer: x = 3 Hide answer | Show step-by-step
• Equation: 2x + 6 = 4x - 2 Show answer | Show step-by-step Answer: x = 4 Hide answer | Show step-by-step
• Equation: -x - 1 = 221 + 2x Show answer | Show step-by-step Answer: x = -74 Hide answer | Show step-by-step
• Equation: 15 + 5x = 0 Show answer | Show step-by-step Answer: x = -3 Hide answer | Show step-by-step
• Equation: 17x - 12 = 114 + 3x Show answer | Show step-by-step Answer: x = 9 Hide answer | Show step-by-step
• Equation: 2x - 10 = 10 - 3x Show answer | Show step-by-step Answer: x = 4 Hide answer | Show step-by-step
• Equation: 12x + 0 = 144 Show answer | Show step-by-step Answer: x = 12 Hide answer | Show step-by-step
• Equation: -10x - 19 = 19 - 8x Show answer | Show step-by-step Answer: x = -19 Hide answer | Show step-by-step

## Related Pages

Equation Basics Lesson Brush up on your knowledge of the techniques needed to solve problems on this page.

Equation Calculator Will automatically solve equations and show all of the required work.

Looking for someone to help you with algebra? At Wyzant, connect with algebra tutors and math tutors nearby. Prefer to meet online? Find online algebra tutors or online math tutors in a couple of clicks.

• The height, in meters, above sea level of a NASA launched rocket is given by h ( t ) = − 4.9 t^2 + 301 t + 94
• If Auggie is 2 years older than 6 times Elin's age. The sum of their ages is less than 44. What is the oldest Elin could be? Show all your work.
• Stuck on question
• Stuck on math problem

• My Preferences
• Basic Math & Pre-Algebra
• Study Guides
• Solving Simple Equations
• Multiplying and Dividing Using Zero
• Common Math Symbols
• Quiz: Ways to Show Multiplication and Division, Multiplying and Dividing by Zero, and Common Math Symbols
• Properties of Basic Mathematical Operations
• Quiz: Properties of Basic Mathematical Operations
• Grouping Symbols and Order of Operations
• Groups of Numbers
• Quiz: Groups of Numbers
• Ways to Show Multiplication and Division
• Order of Operations
• Quiz: Grouping Symbols and Order of Operations
• Estimating Sums, Differences, Products, and Quotients
• Quiz: Estimating Sums, Differences, Products, and Quotients
• Divisibility Rules
• Quiz: Divisibility Rules
• Factors, Primes, Composites, and Factor Trees
• Place Value
• Quiz: Factors, Primes, Composites, and Factor Trees
• Quiz: Place Value
• Using the Place Value Grid
• Quiz: Using the Place Value Grid
• Decimal Computation
• Quiz: Decimal Computation
• What Are Decimals?
• Repeating Decimals
• Proper and Improper Fractions
• Mixed Numbers
• Renaming Fractions
• Quiz: Proper and Improper Fractions, Mixed Numbers, and Renaming Fractions
• What Are Fractions?
• Quiz: Factors and Multiples
• Adding and Subtracting Mixed Numbers
• Quiz: Adding and Subtracting Fractions and Mixed Numbers
• Multiplying Fractions and Mixed Numbers
• Dividing Fractions and Mixed Numbers
• Quiz: Multiplying and Dividing Fractions and Mixed Numbers
• Simplifying Fractions and Complex Fractions
• Quiz: Simplifying Fractions and Complex Fractions
• Changing Fractions to Decimals
• Changing Terminating Decimals to Fractions
• Changing Infinite Repeating Decimals to Fractions
• Quiz: Changing Fractions to Decimals, Changing Terminating Decimals to Fractions, and Changing Infinite Repeating Decimals to Fractions
• Applications of Percents
• Quiz: Applications of Percents
• Changing Percents, Decimals, and Fractions
• Important Equivalents
• Quiz: Changing Percents, Decimals, and Fractions, and Important Equivalents
• Quiz: Rationals (Signed Numbers Including Fractions)
• Quiz: Integers
• Rationals (Signed Numbers Including Fractions)
• Quiz: Square Roots and Cube Roots
• Powers and Exponents
• Quiz: Powers and Exponents
• Square Roots and Cube Roots
• Quiz: Scientific Notation
• Powers of Ten
• Quiz: Powers of Ten
• Scientific Notation
• Metric System
• Converting Units of Measure
• Quiz: U.S. Customary System, Metric System, and Converting Units of Measure
• Significant Digits
• Quiz: Precision and Significant Digits
• U.S. Customary System
• Calculating Measurements of Basic Figures
• Quiz: Calculating Measurements of Basic Figures
• Quiz: Bar Graphs
• Line Graphs
• Quiz: Line Graphs
• Circle Graphs or Pie Charts
• Introduction to Graphs
• Quiz: Circle Graphs or Pie Charts
• Coordinate Graphs
• Quiz: Coordinate Graphs
• Quiz: Statistics
• Probability
• Quiz: Probability
• Arithmetic Progressions
• Geometric Progressions
• Quiz: Arithmetic Progressions and Geometric Progressions
• Quiz: Variables and Algebraic Expressions
• Quiz: Solving Simple Equations
• Variables and Algebraic Expressions
• Quiz: Solving Process and Key Words
• Solving Process
• Basic Math Quizzes

Solving an equation is the process of getting what you're looking for, or  solving for , on one side of the equals sign and everything else on the other side. You're really sorting information. If you're solving for  x , you must get x  on one side by itself.

Some equations involve only addition and/or subtraction.

Solve for  x .

x  + 8 = 12

To solve the equation  x  + 8 = 12, you must get  x  by itself on one side. Therefore, subtract 8 from both sides.

Solve for  y .

y  – 9 = 25

To solve this equation, you must get  y  by itself on one side. Therefore, add 9 to both sides.

To check, simply replace  y  with 34:

x  + 15 = 6

To solve, subtract 15 from both sides.

To check, simply replace  x  with –9 :

Notice that in each case above,  opposite operations  are used; that is, if the equation has addition, you subtract from each side.

Multiplication and division equations

Some equations involve only multiplication or division. This is typically when the variable is already on one side of the equation, but there is either more than one of the variable, such as 2  x , or a fraction of the variable, such as

In the same manner as when you add or subtract, you can multiply or divide both sides of an equation by the same number,  as long as it is not zero , and the equation will not change.

Divide each side of the equation by 3.

To check, replace  x  with 3:

To solve, multiply each side by 5.

To check, replace  y  with 35:

Or, without canceling,

Combinations of operations

Sometimes you have to use more than one step to solve the equation. In most cases, do the addition or subtraction step first. Then, after you've sorted the variables to one side and the numbers to the other, multiply or divide to get only one of the variables (that is, a variable with no number, or 1, in front of it:  x , not 2  x ).

2  x  + 4 = 10

Subtract 4 from both sides to get 2  x  by itself on one side.

Then divide both sides by 2 to get  x .

5x  – 11 = 29

Divide each side by 5.

To check, replace  x  with 8:

Subtract 6 from each side.

To check, replace  x  with 9:

To check, replace  y  with –25:

3  x  + 2 =  x  + 4

Subtract 2 from both sides (which is the same as adding –2).

Subtract  x  from both sides.

Note that 3  x  –  x  is the same as 3  x  – 1  x .

Divide both sides by 2.

To check, replace  x  with 1:

5  y  + 3 = 2  y  + 9

Subtract 3 from both sides.

Subtract 2  y  from both sides.

Divide both sides by 3.

To check, replace  y  with 2:

Sometimes you need to simplify each side (combine like terms) before actually starting the sorting process.

Solve for  x .

3  x  + 4 + 2 = 12 + 3

First, simplify each side.

Subtract 6 from both sides.

To check, replace  x  with 3:

4  x  + 2  x  + 4 = 5  x  + 3 + 11

Simplify each side.

6  x  + 4 = 5  x  + 14

Subtract 4 from both sides.

Subtract 5  x  from both sides.

To check, replace  x  with 10:

Previous Quiz: Variables and Algebraic Expressions

Next Quiz: Solving Simple Equations

• Online Quizzes for CliffsNotes Basic Math and Pre-Algebra Quick Review, 2nd Edition

Removing #book# from your Reading List will also remove any bookmarked pages associated with this title.

Are you sure you want to remove #bookConfirmation# and any corresponding bookmarks?

MATH CHEMISTRY PHYSICS BIOLOGY EDUCATION

## Solving for x – the essence of algebra

Solving for x means isolating x (or whatever the variable of interest – it doesn't have to be called x ) – on one side of the equal sign (it doesn't matter which).

The way I like to think about the process of solving for x is that I need to "peel away" everything that's in some way "stuck" to it, in order to come up with an equation, at the end, that says " x = (something)".

Let's discover how to do this with examples. First the easy stuff, then we'll do more difficult problems.

I'll only give some basics here. As you learn more about algebra, you'll be able to solve for variables in many other more interesting and challenging situations.

Here's a little cartoon showing what I mean. Our job will be to clear all of the junk away from x in order to see what it really is.

## Inverse operations

In this section, we'll refer often to inverse operations. Inverse operations are opposite, and one can be used to undo the action of the other.

• Addition and subtraction are inverse operations.
• Multiplication and division are inverse operations.

For our first example, we'll solve for x when some number is added to it. Here's such an equation:

What needs to be done to isolate the variable x on the left side is to "move" that 3 over to the right. That's accomplished by subtracting a 3 from both sides. Remember, we have to do the same thing to both sides , unless it doesn't have an un-balancing consequence, like adding zero or multiplying by 1.

Until you get used to doing this kind of small thing in your head, you might want to write it out like this:

Now it's just some arithmetic to get the answer:

You can check to see if this is the correct value of x, by simply substituting 6 for x in the original algebraic equation:

## More simple addition & subtraction

Let's do the same kind of equation, but this time x has something subtracted from it. Right away we know that the method for solving this problem is the same, because subtraction is just addition of a negative. Here's the problem

We need to get rid of the 8 on the left by "moving it" to the right side. It is subtracted from x , so we use addition to move it to the right.

Here's how you can write it out explicitly. -8 + 8 = 0 on the left:

Then the final arithmetic to get the value of x :

## Multiplication & division

What about if x is multiplied by something.? Well, it's not that different. We just get rid of the multiplier using the inverse operation of multiplication, division . Here's our example:

We'll move the 3 to the right side by dividing 3 into both the left and right sides of the equation. If what's on the left is equal to what's on the right, then 1/3 of each must also be equal.

You can write it out like this, and "cancel" the 3's on the left:

Remember that "cancelling" is just understanding that 3/3 = 1. Then just do the division on the right (12/3) to get the solution:

Once again, we can plug our value for x into the original equation to check it:

The situation is very similar when x is divided by a constant. Here's an example:

x is divided by 7. The inverse operation of division is multiplication, so we'll multiply both sides of the equation by 7 to move that 7 to the right side:

The 7's on the left cancel, which is just to say that 7/7 = 1.

Now 7(2) is 14, so we have

Looking back at the original equation, we see that 14 divided by 7 is 2, so our answer is correct.

## Combinations of operations

Now let's do some combinations of these moves. In this example the variable x has something multiplying it and something added to that:

We'll need two steps to liberate the x this time. Do the easy one first, and add the 5 to both sides to move it to the right. Then "divide away" the 4.

First the addition to move the 5:

Here's the intermediate result:

Then divide both sides by 4, canceling the 4's on the left

and complete the arithmetic.

I'll leave the answer like that. I think it's unfortunate that this kind of fraction has been called "improper." There's nothing wrong with it, and in fact in mathematics, it's preferred over the compound fraction 4-½.

Here's another combination example:

This time we'll need to move the three (first – it's the easiest) by subtraction, then the 4 by multiplication (the inverse of division).

Here's how the 3 gets moved:

And here we get rid of the 4 on the left to isolate x :

And the result is:

## Complicated situations: Reverse PEMDAS

Notice that in the last two examples, we chose to do the subtraction and addition parts before the addition or multiplication. Let's try one of those again:

But this time we'll divide by the 4 first, then do our addition to get x alone. First the division, noting that in this case we have to divide all three terms of the equation by 4:

The result is

Now we move the 5/4 to the right side to find x :

which is the same result we got above. But ... it was a bit more cumbersome than just doing it the easy way from the beginning. These can get more complicated, too, so it's important to get the order right.

You know about order of operations (we gave it the acronym PEMDAS ) if you read the algebra basics section, and it turns out you can't go wrong in solving for x if you just reverse it: " SADMEP ." That means to do the subtraction and addition first, then the division and multiplication, then the exponents and what's inside parenthesis last. Check out examples 5 and 6 above and you'll see that's exactly what we did.

I like to think of solving for x in this way as "picking the low-hanging fruit" first. I do what's easy first, usually addition and subtraction. I keep peeling layers away in this way until I have x isolated.

## What if the variable is in the denominator?

This kind of problem can cause all kinds of confusion, but the basic procedure is easy to remember.Here's the problem:

There's one thing that really needs to be done in such a problem, and that's to get the variable out of the denominator. Always remember that:

To remove x from the denominator, we multiply both sides by x . The x 's on the left will cancel (x/x = 1), and the x on the right is now in the numerator of 8x .

Now it's a straightforward process to isolate x on the right side:

You can check this answer in the original equation if you remember that dividing by 1/8 is the same as multiplying by the reciprocal of 1/8, which is 8.

## Practice problems

Solve for x in each of the equations below:

## Problem 12 solution

Problem 13 solution.

## Problem 30 solution

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Praxis Core Math

Course: praxis core math   >   unit 1.

• Algebraic properties | Lesson
• Algebraic properties | Worked example
• Solution procedures | Lesson
• Solution procedures | Worked example
• Equivalent expressions | Lesson
• Equivalent expressions | Worked example
• Creating expressions and equations | Lesson
• Creating expressions and equations | Worked example

## Algebraic word problems | Lesson

• Algebraic word problems | Worked example
• Linear equations | Lesson
• Linear equations | Worked example
• Quadratic equations | Worked example

## What are algebraic word problems?

What skills are needed.

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

## How do we solve algebraic word problems?

• Define a variable.
• Write an equation using the variable.
• Solve the equation.
• If the variable is not the answer to the word problem, use the variable to calculate the answer.

## What's a Venn diagram?

• an integer, like 6 ‍
• a simplified proper fraction, like 3 / 5 ‍
• a simplified improper fraction, like 7 / 4 ‍
• a mixed number, like 1   3 / 4 ‍
• an exact decimal, like 0.75 ‍
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍
• (Choice A)   \$ 4 ‍   A \$ 4 ‍
• (Choice B)   \$ 5 ‍   B \$ 5 ‍
• (Choice C)   \$ 9 ‍   C \$ 9 ‍
• (Choice D)   \$ 14 ‍   D \$ 14 ‍
• (Choice E)   \$ 20 ‍   E \$ 20 ‍
• (Choice A)   10 ‍   A 10 ‍
• (Choice B)   12 ‍   B 12 ‍
• (Choice C)   24 ‍   C 24 ‍
• (Choice D)   30 ‍   D 30 ‍
• (Choice E)   32 ‍   E 32 ‍
• (Choice A)   4 ‍   A 4 ‍
• (Choice B)   10 ‍   B 10 ‍
• (Choice C)   14 ‍   C 14 ‍
• (Choice D)   18 ‍   D 18 ‍
• (Choice E)   22 ‍   E 22 ‍

## Things to remember

Want to join the conversation.

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

#### IMAGES

1. Algebra solve for x problems

2. Solving for “x”

3. 😎 Algebra solve for x problems. Equation Calculator & Solver. 2019-02-15

4. Math Worksheets Solving For X Math Worksheets

5. Solving for x by adding and subtracting: Example Problems

6. Pre Algebra solving for x

#### VIDEO

1. solving x^5=20 vs 5^x=20, know the difference!

2. A Nice Math Algebra Problem , to find the value of x and y

3. A Nice Algebra Problem • X=?

4. Linear equation with one unknown: Solve x/3+10=14 step-by-step solution

5. Algebra Help: Solve for x√((x-2)^(-3) )=64

6. A Very Interesting Equation

1. What Are the Six Steps of Problem Solving?

The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

2. How to Solve Common Maytag Washer Problems

Maytag washers are reliable and durable machines, but like any appliance, they can experience problems from time to time. Fortunately, many of the most common issues can be solved quickly and easily. Here’s a look at how to troubleshoot som...

3. Sudoku for Beginners: How to Improve Your Problem-Solving Skills

Are you a beginner when it comes to solving Sudoku puzzles? Do you find yourself frustrated and unsure of where to start? Fear not, as we have compiled a comprehensive guide on how to improve your problem-solving skills through Sudoku.

4. Solve for X

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the

5. Practice Solving Equations

Practice Solving Equations. Names: Solve each: 1). 2). 3). 4). 5). 6). 7). 8). Page 2. 9). 10) Solve for x: 11). 12)

6. 6 Ways to Solve for X

Using Fractions · Step 1 Write down the problem. · Step 2 Cross multiply... · Step 3 Combine like terms. · Step 4 Isolate x by dividing each term by the x

7. SOLVING EQUATIONS

The following table is a partial lists of typical equations. LINEAR EQUATIONS - Solve for x in the following equations. x - 4 = 10 Solution. 2x -

8. Equation Basics Worksheet

9. Solving Simple Equations

If you're solving for x, you must getx on one side by itself. Addition and

10. Solving for x

First the easy stuff, then we'll do more difficult problems. I'll only give some basics here. As you learn more about algebra, you'll be able to solve for

11. Algebra

This pre-algebra video tutorial explains the process of solving two step equations with fractions and variables on both sides ... problems. My

12. Equations with variables on both sides (practice)

Equations with variables on both sides. Problem. Solve for f ‍ . − f + 2 + 4 f = 8 − 3 f ‍. f = ‍. Stuck? Review related articles/videos or use a hint.

13. Solve for x in One Step (Simplifying Math)

In this lesson you can see how to isolate the variable and solve for the variable in one step equations. My recommended Calculators: If you

14. Algebraic word problems

Solving linear equations with one variable; Evaluating algebraic expressions; Solving problems using Venn diagrams. How do we solve algebraic word problems?