Solve a linear inequality

Steps

1. Solve exactly like an equation: expand, move terms, collect.
2. If you multiply or divide by a negative number, flip the sign.
3. Draw the number line: hollow circle for > or <, solid dot for ≥ or ≤.
4. For "greatest integer" or "least integer", read it off the number line.

Why the flip: 3 > 2, but −3 < −2. Multiplying by −1 swaps the order of numbers on the number line.

Safer habit: move the x-terms to the side where the coefficient stays positive, so you never divide by a negative.

Worked examples

−2x > 4
  x < −2      divide by −2, flip

For the whole topic, read Linear inequalities in one unknown: key points, common mistakes and how the DSE tests it.