Solve like an equation, but flip when × or ÷ by a negative
Treat the inequality as an equation, except reverse the inequality sign whenever you multiply or divide both sides by a negative number.
Quadratic inequalities: factorise then sketch
Find the critical values (roots), sketch the parabola, and read off where it is above () or below () the -axis.
Regions: draw, label and shade
Draw each boundary line, decide which side satisfies each inequality, and shade the overlap. A solid line for , dashed for .
Drawn from real examiner reports.
Forgetting to reverse the sign with a negative coefficient
With a negative - or -coefficient, students keep the original sign, or even replace the inequality with an equals sign or a bare number.
Giving the wrong region for a quadratic inequality
Quoting when the answer is or (or vice versa); not sketching, or working backwards from a calculator and writing factors that do not expand to the given quadratic.
Inaccurate or unlabelled boundary lines
Drawing the line for through the wrong intercepts, or not labelling lines and indicating the shaded region.
Make sure the final answer is an inequality
After all the algebra, write the answer with the correct inequality sign — not an equals sign or a single number.
Solve exactly like an equation — but reverse the sign when you multiply or divide both sides by a negative: Your final answer must be an inequality, not "" or a lone number.
When do you reverse an inequality sign?
Solve .
