Inequalities

Inequalities tell us about a range of values, rather than one specific solution. This lesson covers solving linear inequalities, representing solutions on number lines and using set notation, graphical inequalities (Higher), and quadratic inequalities (Higher).

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Key Vocabulary

Symbol	Meaning
<	Less than
>	Greater than
≤	Less than or equal to
≥	Greater than or equal to

Term	Meaning
Inequality	A mathematical statement comparing two expressions using <, >, ≤, or ≥
Integer values	Whole numbers (positive, negative, or zero)
Set notation	e.g. {x : x > 3} meaning "the set of all x such that x is greater than 3"

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Solving Linear Inequalities

Solve exactly like a linear equation — with one important rule: if you multiply or divide by a negative number, you must reverse the inequality sign.

Worked Example 1

Solve: 3x + 5 > 14

3x > 9

x > 3

Worked Example 2

Solve: 7 − 2x ≤ 3

−2x ≤ −4