Free Interactive Pre-Algebra Tool

Evaluating Algebraic Expressions

Replace variables with their given values, simplify the resulting numerical expression, and explain each step as you work.

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Need Help Evaluating Expressions?

Learn How Substitution Works

Review variables, coefficients, substitution, parentheses, order of operations, and worked examples.

Read the Evaluating Expressions Guide

How It Works

Turn Variables Into Numbers One Step at a Time

Evaluating an expression means replacing each variable with its assigned value and then simplifying the numerical expression using the order of operations.

1

Read the Expression

Identify every variable, coefficient, operation, exponent, and grouping symbol.

2

Substitute the Values

Replace each variable with its given number. Use parentheses around negative values.

3

Simplify Carefully

Follow the order of operations after all variables have been replaced.

4

Check the Result

Make sure every variable was replaced and every operation was completed correctly.

Interactive Practice

Substitute, Simplify, and Evaluate

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Problems 0
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Evaluate the Expression

Medium

Substitute the given value for each variable, then simplify the numerical expression.

3x + 2
x = 5
Replace x with 5 before completing any arithmetic.
  1. 1 Identify
  2. 2 Substitute
  3. 3 Simplify
  4. 4 Evaluate
1

Read the Problem

Match Each Variable With Its Value

Current Step

Current Problem

Medium

Substitute the given value for each variable, then simplify.

3x + 2
x = 5

Which value should replace the highlighted variable?

2

Replace the Variable

Write the Substituted Expression

Locked

Current Problem

Medium

Substitute the given value for each variable, then simplify.

3x + 2
x = 5

Replace every variable with its assigned value. Use parentheses around negative values.

3

Complete the Arithmetic

Simplify the Numerical Expression

Locked

Current Problem

Medium

Substitute the given value for each variable, then simplify.

3x + 2
x = 5

Complete the multiplication, exponent, or grouped operation that comes first.

4

Finish the Evaluation

Enter the Final Value

Locked

Current Problem

Medium

Substitute the given value for each variable, then simplify.

3x + 2
x = 5

Complete the remaining arithmetic and enter the value of the expression.

Keep This Nearby

Evaluating Expressions Reference

Substitute first. Then use the order of operations.

Variable A letter that represents a number In 3x + 2, x is the variable
Coefficient A number multiplying a variable In 3x, the coefficient is 3
Substitution Replace a variable with its given value x = 5 → 3(5) + 2
Negative Values Put substituted negatives in parentheses x = −4 → 2(−4) + 7
Exponents Substitute before evaluating the power x = 3 → x² = (3)² = 9
Order of Operations Grouping, exponents, multiply/divide, add/subtract 2(5) + 3 = 10 + 3 = 13

Key Reminders

Avoid the Most Common Substitution Mistakes

Check these details before submitting your answer.

Replace Every Variable

A completed substitution should not contain any of the original variables.

4x − 1 with x = 3 becomes 4(3) − 1

Keep the Operations

Substitution changes the variable, not the operation connecting the terms.

5y means 5 × y, so y = 2 gives 5(2)

Use Parentheses for Negatives

Parentheses make the sign of a substituted negative value clear.

x = −3 → x² = (−3)² = 9

Simplify After Substituting

Do not perform arithmetic until the variables have been replaced.

2x + 6 with x = 4 → 2(4) + 6 → 14

Keep Learning

Understand Why Substitution Works

Review variables, coefficients, terms, substitution, negative values, exponents, and complete worked examples in the companion guide.

Read the Evaluating Expressions Guide