Skip to Content

Log in / Sign up

wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow

How to Evaluate an Algebraic Expression

Download Article

Co-authored by Taylor Klein

Last Updated: January 16, 2024 Fact Checked

Download Article

Evaluating an algebraic expression means to calculate the expression given a certain variable. Sometimes a problem will ask you to do this; most of the time, however, you will want to evaluate an expression to check your own algebra work. As long as you understand the basic terms and rules of algebra, evaluating an expression is a simple process.

Part 1

Part 1 of 3:

Understanding an Expression

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/df\/Evaluate-an-Algebraic-Expression-Step-1-Version-2.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/d\/df\/Evaluate-an-Algebraic-Expression-Step-1-Version-2.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Identify the parts of an algebraic expression. An algebraic expression is a set of numbers and letters combined by mathematical operations, such as addition, subtraction, division, and multiplication. The numbers in the expression are called constants or coefficients, depending on their function. The letters are called variables. ^{[1]
X
Research source}
- $2x$ is an expression. In this expression, you are multiplying the coefficient $2$ by the variable $x$ .
- $2x+3y$ is an expression called a binomial. In this expression, you add the product of $3y$ to the product of $2x$ . In this expression, $2$ and $3$ are coefficients, and $x$ and $y$ are variables.
- Once you add an equal sign to an expression, it becomes an equation. For example, $2x=14$ is an equation.
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e0\/Evaluate-an-Algebraic-Expression-Step-2-Version-2.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-2-Version-2.jpg","bigUrl":"\/images\/thumb\/e\/e0\/Evaluate-an-Algebraic-Expression-Step-2-Version-2.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

A variable is a letter that represents any number. Therefore, variables are often used to represent unknown numbers. ^{[2]
X
Research source} In algebra, you are usually trying to find the value of the variable. In order to evaluate an algebraic expression, however, you need to be given the variable’s value.

Advertisement
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f4\/Evaluate-an-Algebraic-Expression-Step-3-Version-2.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-3-Version-2.jpg","bigUrl":"\/images\/thumb\/f\/f4\/Evaluate-an-Algebraic-Expression-Step-3-Version-2.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

3
Determine how to evaluate the expression. Evaluate means to simplify an expression. When you are asked to evaluate an algebraic expression, you need to plug a given value for the variable into the expression and solve. ^{[3]
X
Research source}
- For example, you might be asked to evaluate $2x$ when $x=2$ .

Advertisement

Part 2

Part 2 of 3:

Evaluating an Expression with One or Two Variables

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2e\/Evaluate-an-Algebraic-Expression-Step-4-Version-2.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-4-Version-2.jpg","bigUrl":"\/images\/thumb\/2\/2e\/Evaluate-an-Algebraic-Expression-Step-4-Version-2.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Identify the variable and its value. This information should be given to you. Usually you will be told to evaluate the expression “when” or “where” the variable is equal to a certain value. If you are not given the variable’s value, you cannot evaluate the expression. ^{[4]
X
Research source}
- For example, you might be asked to evaluate the expression $5x-10$ when $x=8$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/48\/Evaluate-an-Algebraic-Expression-Step-5-Version-2.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-5-Version-2.jpg","bigUrl":"\/images\/thumb\/4\/48\/Evaluate-an-Algebraic-Expression-Step-5-Version-2.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

2
Substitute the given value for the variable. To do this, plug the given value into the expression wherever you see the variable. If the variable has a coefficient (a number you need to multiply its value by), make sure to put the value in parentheses. ^{[5]
X
Research source}
- For example, to evaluate $5x-10$ when $x=8$ , replace the $x$ in the equation with $8$ : $5(8)-10$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/3e\/Evaluate-an-Algebraic-Expression-Step-6.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-6.jpg","bigUrl":"\/images\/thumb\/3\/3e\/Evaluate-an-Algebraic-Expression-Step-6.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-6.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

3
Complete the necessary calculations. Remember to follow the order of operations when solving an expression. When you complete your calculations rewrite the expression as an equation. ^{[6]
X
Research source}
- For example:
  $5(8)-10$
  $=40-10$
  $=30$
  So, $5(8)-10=30$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/0f\/Evaluate-an-Algebraic-Expression-Step-7.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-7.jpg","bigUrl":"\/images\/thumb\/0\/0f\/Evaluate-an-Algebraic-Expression-Step-7.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-7.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

4
Evaluate an expression with Two Variables. To do this, follow the same steps as you do for evaluating an expression with one variable, except plug in the values for both variables into the equation. These values should be given. ^{[7]
X
Research source}
- Make sure you do not switch the values. The $x$ value cannot be substituted for the $y$ variable and vice versa. Doing so will give you an incorrect solution.

Advertisement

Part 3

Part 3 of 3:

Completing Sample Problems

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e8\/Evaluate-an-Algebraic-Expression-Step-8.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-8.jpg","bigUrl":"\/images\/thumb\/e\/e8\/Evaluate-an-Algebraic-Expression-Step-8.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

1
Evaluate the following expression when $x=3$ : $2x+3$ .
- Identify the variable and its value. The variable is $x$ , and you are evaluating the expression for $x=3$ .
- Substitute the given value for the variable: $2(3)+3$ .
- Make the necessary calculations: $2(3)+3=6+3=9$ .
- Write the equation: $2(3)+3=9$
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/73\/Evaluate-an-Algebraic-Expression-Step-9.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-9.jpg","bigUrl":"\/images\/thumb\/7\/73\/Evaluate-an-Algebraic-Expression-Step-9.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

2
Evaluate the following expression with two variables when $x=2$ and $y=6$ : $4x+3y$ .
- Identify both variables and their values. The variables are $x$ and $y$ , and you are evaluating the expression for $x=2$ and $y=6$ .
- Substitute both given values for the variables: $4(2)+3(6)$ .
- Make the necessary calculations: $4(2)+3(6)=8+18=26$ .
- Write the equation: $4(2)+3(6)=26$ .
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/05\/Evaluate-an-Algebraic-Expression-Step-10.jpg\/v4-460px-Evaluate-an-Algebraic-Expression-Step-10.jpg","bigUrl":"\/images\/thumb\/0\/05\/Evaluate-an-Algebraic-Expression-Step-10.jpg\/aid3181794-v4-728px-Evaluate-an-Algebraic-Expression-Step-10.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}

3
Evaluate the following polynomial when $x=4$ : $7x^{{2}}-12x+13$ .
- Identify the variable and its value. The variable is $x$ , and you are evaluating the expression for $x=4$ .
- Substitute the given value for the variable: $7(4)^{{2}}-12(4)+13$ .
- Make the necessary calculations. Remember when working with exponents that you should calculate the exponent before multiplying by a coefficient:
  $7(4)^{{2}}-12(4)+13$
  $=7(16)-12(4)+13$
  $=112-48+13$
  $=64+13$
  $=77$
- Write the equation: $7(16)-12(4)+13=77$

Advertisement

Community Q&A

Search

Add New Question

Question

How do I evaluate 10 and -7 ?

Donagan

Top Answerer

10 + (-7) = 10 - 7 = 3.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 13 Helpful 39
Question

If x can have only values -3, 0, and 2, and y can have only the values -4, 2, and 3, what is the greatest possible value for 2x + y^2?

Community Answer

Use 2, the highest positive value of x, and -4, the highest absolute value of y (because it's squared), and evaluate the expression.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 13 Helpful 25
Question

How do I write the sum of a, b and c?

Donagan

Top Answerer

a + b + c.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 14 Helpful 25

See more answers

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Advertisement

Video

Tips

Submit a Tip

All tip submissions are carefully reviewed before being published

Thanks for submitting a tip for review!

Related Articles

How to Use Equations
How to Solve a Simple Linear Equation
How to Write an Algebraic Expression
How to Get Your Child Ready for Algebra

You Might Also Like

Advertisement

Expert Interview

Thanks for reading our article! If you’d like to learn more about math, check out our in-depth interview with Taylor Klein .

References

About This Article

Co-authored by:

Advanced Math Teacher

This article was co-authored by Taylor Klein . Taylor Klein is an Advanced Math Teacher based in Philadelphia, Pennsylvania. She has worked in the education field for over 10 years, including eight years as a middle school Advanced Math Teacher. She has a master’s degree in Instructional Technology and Design and a master’s degree in Educational Leadership and Administration. This article has been viewed 142,535 times.

3 votes - 80%

Co-authors: 12

Updated: January 16, 2024

Views: 142,535

Categories: Algebra

In other languages

Thanks to all authors for creating a page that has been read 142,535 times.

Reader Success Stories

Giyeth Berondo

Jul 30, 2017

"It really helped me understand how to multiply mixed fractions."

More reader stories Hide reader stories

Share your story

Did this article help you?

Advertisement

X

-

-

519

.mwimg a.image{display:none}#header_logo{display:none}#cse-search-box{display:none}#cse-search-box-noscript{display:block !important}#cse-search-box-noscript .cse_q{color:#FFF;background-color:#B3CE9C}.wh_search .cse_q{width:88%}#mw-mf-main-menu-button{display:none;visibility:hidden}.header .search{display:none}#search_footer .cse_sa{background-image:url(/extensions/wikihow/mobile/images/white_mag.png);background-size:22px}.related_box{display:block;background:#EEE;border:5px solid #FFF;vertical-align:bottom;width:127px;background-size:180px;float:left;height:120px;position:relative}.related_box p{line-height:15px !important;font-size:13px;background-color:rgba(67,95,44,.4);color:#FFF;font-weight:bold;padding:8px;margin:0 !important;position:absolute;bottom:0}#noscript_header_logo{display:table-cell;vertical-align:middle;background-position:50% 77%;background-repeat:no-repeat;background-image:url(/extensions/wikihow/mobile/images/wikihow_logo_230.png);background-size:105px;width:auto;height:51px;padding:0 14px}.articleinfo{display:none}#iorg_free_data{z-index:50;width:100%;position:fixed}#ara_recommendations{display:none}

Design a Mobile Website

View Site in Mobile | Classic

Share by: