This module covers inequalities: solving a linear inequality, showing the answer on a number line, drawing a boundary on a graph, combining several constraints into a feasible region, and checking whether a point obeys them all. The skills link algebra to graphs and appear in word problems about limits and budgets.
Check the current Cambridge IGCSE Mathematics 0580 syllabus for the exact wording in your exam year, because content can differ between Core and Extended routes and between syllabus versions. Our Mathematics learning guide shows where this module sits among the others.
What should you already know?
You should be able to solve a one-step and two-step linear equation, handle negative numbers, and plot a straight line from two points. The earlier modules on equations and formulas and simultaneous relationships cover these skills.
An orienting example
Find the integers that satisfy −1 < x and 10 − 2x ≥ 4.
Step 1, solve the second inequality: subtract 10: −2x ≥ −6. Divide by −2 and reverse the sign: x ≤ 3.
Step 2, combine with the first: −1 < x and x ≤ 3 gives −1 < x ≤ 3.
Step 3, list the integers: −1 is excluded and 3 is included, so 0, 1, 2 and 3.
Step 4, check: x = 3 gives 10 − 6 = 4, and 4 ≥ 4 is true. x = 4 gives 2, and 2 ≥ 4 is false.
Picture: in one variable the answer is a stretch of the number line. In two variables it becomes a region of the graph. Both ideas use the same three questions: where is the boundary, is the boundary included, and which side is wanted?
In which order should you study it?
- Reverse an inequality when multiplying by a negative: the one rule that separates inequalities from equations.
- Represent an interval on a number line: open and closed circles, and integer lists.
- Draw a boundary for a linear inequality: solid or dashed lines, and the test-point method for shading.
- Identify a feasible region from combined constraints: overlap, corners and integer points.
- Check whether a proposed point satisfies every constraint: the algebra test that works without a graph.
Then work through the mixed practice set. A steady pace is one lesson an evening, then the practice set at the weekend.
Which traps catch most students here?
- Forgetting to reverse the sign when dividing by a negative.
- Swapping open and closed circles, so an end-point is included or excluded wrongly.
- Using a solid line for < or >, or a dashed line for ≤ or ≥.
- Shading by the rule “less than means below” without testing a point.
- Keeping the union instead of the overlap when combining constraints.
- Stopping after the first true statement when checking a point.
Each lesson shows one of these slips in full and then corrects it.
How should you use the practice set?
Attempt each question on paper and write the working as you would in an exam. A substitution check at the end takes seconds and catches most sign errors. The non-calculator working trainer lets you test arithmetic steps without reaching for a calculator.
When you get something wrong, use the routing table at the end of the practice set to return to the right lesson. Record the slip in the mistake log, and retry a fresh question a few days later.
If you want teaching beyond self-study, online one-to-one Mathematics tuition means an experienced teacher reads your written working and finds the habit behind the error.