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 .
Flip the sign only 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.
Drawn from real examiner reports.
Not reversing the sign on a negative
With a negative - or -coefficient, students keep the original sign, or even replace the inequality with an equals sign or a bare number.
A commonly reported examiner note records this on a recent higher-tier paper.
Inaccurate or unlabelled boundary lines
Drawing the line for through the wrong intercepts, or not labelling lines and indicating the shaded region.
A commonly reported examiner note records this on a recent higher-tier paper.
Flipping the sign at the wrong step
Only multiplying or dividing both sides by a negative reverses the inequality. Subtracting a term does not: from , subtracting keeps to give ; the flip happens only when you then divide by , giving .
Losing strict vs inclusive ends
Keep and straight through the working. Solving gives : the lower end stays strict and the upper end inclusive. Writing wrongly includes .
Shading the wrong side of a line
Without testing a point, students shade the wrong side or use the wrong line style. Test a point off the line (often the origin) to pick the side, and use a solid line for but a dashed line for .
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.
Test a point to choose which side to shade
To decide which side of a boundary line to keep, substitute a point not on the line — the origin is easiest — into the inequality. Shade the side that makes it true (or the unwanted side, if the question asks you to shade that).
Solve a double inequality in one go
For , apply the same step to all three parts at once: add to get , then divide by to get . Splitting it into two separate inequalities invites an endpoint slip.
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.
Solid vs dashed boundary line?
Solve .
