Inequalities

Inequality Symbols

Symbol	Meaning	Example
>	greater than	x > 5
<	less than	x < 3
≥	greater than or equal to	x ≥ 0
≤	less than or equal to	x ≤ 10

Solving Inequalities

Solve like an equation, with one important rule:

⚠️ When you multiply or divide by a negative number, flip the inequality sign.

Example: 2x + 3 < 11 → subtract 3: 2x < 8 → divide by 2: x < 4

With a negative: -3x > 9 → divide by -3 and flip: x < -3

Representing on a Number Line

• Open circle (○) — does not include the value: x > 4
• Closed circle (●) — includes the value: x ≥ 4

○─────────►
4   5   6   (x > 4)

●─────────►
4   5   6   (x ≥ 4)

Compound Inequalities

Two conditions at once:

• -3 ≤ x < 2 means x is between -3 and 2, including -3 but not 2.