Linear Inequalities — O/L Mathematics

What must I remember about Linear Inequalities?

• Inequality relations: < (strictly less than), ≤ (less than or equal to), > (strictly greater than), ≥ (greater than or equal to).
• Solving linear inequalities follows identical steps to linear equations, with one crucial exception regarding signs.
• Sign reversal rule: Multiplying or dividing both sides of an inequality by a negative number REVERSES the direction of the inequality sign (e.g., -2x < 6 ⟹ x > -3).
• Number line representation: Strict inequalities (<, >) use an open, unshaded circle (○); non-strict inequalities (≤, ≥) use a solid, filled circle (●).
• Integer solution sets: Identifying discrete integer values satisfying an inequality (e.g., integer solutions for -2 ≤ x < 3 are {-2, -1, 0, 1, 2}).

Test yourself (1 minute)

1. The forgotten sign reversal trap

   Forgetting to flip the inequality sign when dividing by a negative coefficient (e.g., writing -x > 4 ⟹ x > -4 instead of x < -4) is the most frequent blunder in Paper 1 Part A.

2. Open vs closed circle on number lines

   Drawing a solid dot for < or an open dot for ≤ loses plotting marks.

3. Positive integer requirements

   When questions ask for 'positive integer solutions', exclude 0 and all negative values.

Practise Linear Inequalities questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 24)

What should I study first?

What comes next?

Next in the syllabus

Where does Linear Inequalities fit in the syllabus?

Grade 10 · Term 3