Variables Examples in Math

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

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

Concept Recap

Symbols (usually letters) that represent unknown or changing quantities in mathematical expressions and equations.

Like a box that can hold any number. 'x + 5 = 12' asks: what's in the box?

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: Variables let us write general statements that work for many values.

Common stuck point: Variables aren't fixed numbers — they're flexible placeholders whose value is unknown or allowed to vary.

Sense of Study hint: Try replacing the variable with a few different numbers and see how the expression changes each time.

Worked Examples

Example 1

easy
If x + 5 = 12, what value does x represent?

Solution

  1. 1
    The variable x is a placeholder for an unknown number.
  2. 2
    Subtract 5 from both sides: x = 12 - 5 = 7.
  3. 3
    Check: 7 + 5 = 12 ✓

Answer

x = 7
A variable is a symbol that stands for an unknown value. To find its value, we perform operations that isolate it on one side of the equation.

Example 2

medium
Evaluate the expression 3x + 2y when x = 4 and y = -1.

Practice Problems

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

Example 1

easy
If 2n = 18, what is the value of n?

Example 2

medium
Write an expression using a variable for: 'a number increased by 8.'
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Background Knowledge

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

equalnumber sense