Inequalities on Number Lines and Linear Inequalities
Inequalities compare quantities that are not necessarily equal and can be represented visually.
Symbols and number lines
The symbols <, >, ≤ and ≥ mean less than, greater than, less than or equal to, and greater than or equal to. Use an open circle for < or > and a closed circle for ≤ or ≥. Shade in the direction of values that satisfy the inequality.
Solving rules
Solve inequalities like equations, but reverse the inequality sign whenever both sides are multiplied or divided by a negative number.
Worked examples
- x + 3 < 8 gives x < 5; shade values left of 5 with an open circle.
- 2x ≥ 10 gives x ≥ 5; shade right of 5 with a closed circle.
- −3x < 12 gives x > −4 because division by −3 reverses the sign.
Practice
- Represent x ≤ 2 on a number line.
- Solve 4x − 7 > 9.
- Solve −2x + 5 ≥ 11 and check a test value.
