Evaluation Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Evaluation.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Calculating the value of an expression by substituting specific values for variables.

Plug in the number and compute: if x = 3, then 2x + 1 = 2(3) + 1 = 7.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Evaluation turns abstract expressions into concrete numbers.

Common stuck point: Apply order of operations carefully after substituting — substitute first, then simplify step by step.

Sense of Study hint: Write parentheses around the substituted value every time, especially for negatives: (-3)^2, not -3^2.

Worked Examples

Example 1

easy
Evaluate 5x - 3 when x = 4.

Solution

  1. 1
    Substitute x = 4: 5(4) - 3.
  2. 2
    Multiply: 20 - 3.
  3. 3
    Subtract: 17.

Answer

17
Evaluation means replacing the variable with a given value and computing the result using the order of operations.

Example 2

medium
Evaluate \frac{a^2 - b^2}{a + b} when a = 5 and b = 3.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Evaluate -2x + 10 when x = -3.

Example 2

hard
If f(x) = x^3 - 2x, find f(-2).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

expressionsorder of operations