Grade 10 Maths · Algebra · Paper 1

Linear Inequalities Grade 10

Real Linear Inequalities past paper questions and answers from 2022 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 19 past paper questions
skills: 2 skills
videos: 2 videos

Try a Linear Inequalities exam question

No sign-up. Takes 3 minutes.

Question 2.2 · March 2024 · Provincial · 4 marks

2.2 Solve the inequality

- 2 < 4 + 2 x \leq 6

and represent the solution in interval notation.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Linear Inequalities skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Linear Inequalities Grade 10 questions and answers

Try each one on paper before you open the memo.

4. Question 2.3.1 · March 2025 · Provincial · 3 marks
2.3 Solve the following inequalities
2.3.1 $- 15 < 1 - 4 x < 5$ and $x \in R$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Subtract 1 $- 16 < - 4 x < 4$
  1 mark · Solve a linear inequality
2. ✓
  Divide by -4 and reverse signs $4 > x > - 1$
  1 mark · Solve a linear inequality
3. ✓
  Write in standard notation $- 1 < x < 4$
  1 mark · Solve a linear inequality
5. Question 2.3.1 · March 2025 · Provincial · 2 marks
2.3 Given: $- 9 \leq - 2 x + 3 < 5$
2.3.1 Solve for x.(2)
Show the memo (2 ticks)Memo
1. ✓
  Subtract 3 $- 12 \leq - 2 x < 2$
  1 mark · Solve a linear inequality
2. ✓
  Divide by -2 and flip signs $6 \geq x > - 1$ (or $- 1 < x \leq 6$ )
  1 mark · Solve a linear inequality
6. Question 3.1.2 · June 2025 · Paper 1 · Provincial · 3 marks
3.1 Solve for $x$ if:
3.1.2 $- 3 \leq 2 - x < 0$ , where $x \in R$ and represent your answer on a number line.(3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate the x term $- 3 - 2 \leq - x < 0 - 2$
  $- 5 \leq - x < - 2$
  1 mark · Solve a linear inequality
2. ✓
  Solve for x $5 \geq x > 2$
  Therefore: $2 < x \leq 5$
  1 mark · Solve a linear inequality
3. ✓
  Represent on a number lineThe correct representation is a number line showing an open circle at $2$ and a closed (shaded) circle at $5$ , with a solid line connecting the two values.
  1 mark · Write or draw a solution set
7. Question 3.2.1 · June 2024 · Paper 1 · Provincial · 2 marks
3.2 Given: $2 - \frac{3 x}{4} < 14$
3.2.1 Solve the inequality.(2)
Show the memo (2 ticks)Memo
1. ✓
  Isolate the term with x $- \frac{3 x}{4} < 12$
  1 mark · Solve a linear inequality
2. ✓
  Solve for x (reversing inequality sign) $x > 12 \times (- \frac{4}{3})$
  $x > - 16$
  1 mark · Solve a linear inequality
8. Question 2.1.2 · November 2024 · Paper 1 · Provincial · 4 marks
2.1 Solve for $x$ :
2.1.2 $\frac{2 x - 1}{3} \geq 2 x + 1$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Multiply by denominator $2 x - 1 \geq 3 (2 x + 1)$
  1 mark · Clear fractions in an equation
2. ✓
  Expand and simplify $2 x - 1 \geq 6 x + 3$
  1 mark · Multiply out a single bracket
3. ✓
  Group terms $- 4 x \geq 4$
  1 mark · Solve a linear inequality
4. ✓
  Solve for x (reversing inequality) $x \leq - 1$
  1 mark · Solve a linear inequality
9. Question 2.1.4 · March 2023 · Provincial · 4 marks
2.1 Solve for x:
2.1.4 $3 (2 - 3 x) \geq 15$ (4)
Show the memo (4 ticks)Memo
1. ✓
  Simplifying $6 - 9 x \geq 15$ (or $2 - 3 x \geq 5$ )
  1 mark · Solve a linear inequality
2. ✓
  $- 9 x \geq 9$ $- 9 x \geq 9$ or $- 3 x \geq 3$
  1 mark · Solve a linear inequality
3. ✓
  Answer $x \leq - 1$
  1 mark · Solve a linear inequality
4. ✓
  Number lineClosed dot at $- 1$ , arrow pointing to the left
  1 mark · Write or draw a solution set
10. Question 3.1.3 · March 2022 · Provincial · 4 marks
3.1 Solve for x:
3.1.3 $- 4 \leq 3 x - 1 \leq 5$ (represent your answer graphically)(4)
Show the memo (4 ticks)Memo
1. ✓
  Add 1 to all sides $- 3 \leq 3 x \leq 6$
  1 mark · Solve a linear inequality
2. ✓
  Lower end point -1 $- 1 \leq x$
  1 mark · Solve a linear inequality
3. ✓
  Upper end point 2 $x \leq 2$
  $- 1 \leq x \leq 2$
  1 mark · Solve a linear inequality
4. ✓
  Graphical representationNumber line with closed circles at -1 and 2, line connected.
  1 mark · Write or draw a solution set

Linear Inequalities Grade 10 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

2) Number line interval set builder | Part 1Kevinmathscience

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills