Inequalities Examples in Math

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

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

Concept Recap

Mathematical statements comparing expressions using <, >, \leq, or \geq.

Instead of 'equals exactly,' it's 'at least,' 'at most,' or 'greater/less than.'

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: Inequalities describe ranges of valid solutions, not single values.

Common stuck point: Always flip the inequality symbol when multiplying or dividing both sides by a negative number.

Sense of Study hint: Pick a number from your solution range and a number outside it, then test both in the original inequality.

Worked Examples

Example 1

easy
Solve 2x + 5 > 11.

Solution

  1. 1
    Subtract 5 from both sides: 2x > 6.
  2. 2
    Divide both sides by 2: x > 3.
  3. 3
    The solution is all values greater than 3.

Answer

x > 3
Solving inequalities follows the same steps as equations, with one key difference: multiplying or dividing by a negative number reverses the inequality sign.

Example 2

medium
Solve -3x + 4 \leq 13.

Practice Problems

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

Example 1

easy
Solve x - 4 < 10.

Example 2

hard
Solve 4 - 2x \geq 10.
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Background Knowledge

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

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