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About Inequalities — Class 8 IB

Solve and graph linear inequalities in one and two variables. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 13). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Inequalities — solved examples for Class 8 IB

Example 1easy

Solve: \(x + 3 > 7\)
  1. A)\(x > 4\)
  2. B)\(x > 10\)
  3. C)\(x < 4\)
  4. D)\(x > 3\)

Step-by-step solution

  1. x + 3 > 7
  2. x > 7 − 3
  3. x > 4

Answer: \(x > 4\)

Example 2medium

Solve: \(3x - 7 > 5x + 1\)
  1. A)\(x < -4\)
  2. B)\(x > -4\)
  3. C)\(x < 4\)
  4. D)\(x > 4\)

Step-by-step solution

  1. 3x − 7 > 5x + 1
  2. 3x − 5x > 1 + 7
  3. −2x > 8
  4. x < −4 (flip)

Answer: \(x < -4\)

Example 3hard

Solve: \(x^2 - 5x + 6 > 0\)
  1. A)\(x < 2\) or \(x > 3\)
  2. B)\(2 < x < 3\)
  3. C)\(x > 2\)
  4. D)\(x < 3\)

Step-by-step solution

  1. (x − 2)(x − 3) > 0
  2. Both positive: x > 3
  3. Both negative: x < 2
  4. Solution: x < 2 or x > 3

Answer: \(x < 2\) or \(x > 3\)

Practice questions on Inequalities

  1. Q1.easy

    Solve: \(x - 5 \leq 10\)
    1. A)\(x \leq 15\)
    2. B)\(x \leq 5\)
    3. C)\(x < 15\)
    4. D)\(x \geq 15\)
    Show answer

    Answer: \(x \leq 15\)

    Hint: Add 5 to both sides.

  2. Q2.easy

    Solve: \(2x > 12\)
    1. A)\(x > 6\)
    2. B)\(x > 24\)
    3. C)\(x > 10\)
    4. D)\(x < 6\)
    Show answer

    Answer: \(x > 6\)

    Hint: Divide both sides by 2.

  3. Q3.easy

    Solve: \(3x + 1 < 16\)
    1. A)\(x < 5\)
    2. B)\(x < 6\)
    3. C)\(x \leq 5\)
    4. D)\(x > 5\)
    Show answer

    Answer: \(x < 5\)

    Hint: Subtract 1, then divide by 3.

  4. Q4.medium

    Solve the compound inequality: \(-2 < 3x + 1 \leq 10\)
    1. A)\(-1 < x \leq 3\)
    2. B)\(-1 \leq x < 3\)
    3. C)\(-1 < x < 3\)
    4. D)\(0 < x \leq 3\)
    Show answer

    Answer: \(-1 < x \leq 3\)

    Hint: Subtract 1 from all three parts, then divide by 3.

  5. Q5.medium

    Solve: \(4(x - 2) \leq 3(x + 1)\)
    1. A)\(x \leq 11\)
    2. B)\(x \leq 5\)
    3. C)\(x \geq 11\)
    4. D)\(x \leq -5\)
    Show answer

    Answer: \(x \leq 11\)

    Hint: Expand both sides: 4x − 8 ≤ 3x + 3.

  6. Q6.medium

    Find the integer values of \(x\) satisfying \(-5 \leq 2x - 1 < 7\).
    1. A)-2, -1, 0, 1, 2, 3
    2. B)-2, -1, 0, 1, 2
    3. C)-1, 0, 1, 2, 3
    4. D)-2, -1, 0, 1, 2, 3, 4
    Show answer

    Answer: -2, -1, 0, 1, 2, 3

    Hint: Solve: −5 ≤ 2x − 1 → −4 ≤ 2x → −2 ≤ x. And 2x − 1 < 7 → 2x < 8 → x < 4.

  7. Q7.hard

    Solve: \(x^2 - 4x - 5 \leq 0\)
    1. A)\(-1 \leq x \leq 5\)
    2. B)\(x \leq -1\) or \(x \geq 5\)
    3. C)\(-5 \leq x \leq 1\)
    4. D)\(x < -1\) or \(x > 5\)
    Show answer

    Answer: \(-1 \leq x \leq 5\)

    Hint: Factor: (x − 5)(x + 1) ≤ 0. This is ≤ 0 when the factors have opposite signs.

  8. Q8.hard

    Solve: \(|2x - 3| \leq 7\)
    1. A)\(-2 \leq x \leq 5\)
    2. B)\(x \leq 5\)
    3. C)\(x \geq -2\)
    4. D)\(-5 \leq x \leq 2\)
    Show answer

    Answer: \(-2 \leq x \leq 5\)

    Hint: |2x − 3| ≤ 7 means −7 ≤ 2x − 3 ≤ 7.

  9. Q9.hard

    Solve: \(|3x + 1| > 10\)
    1. A)\(x > 3\) or \(x < -\frac{11}{3}\)
    2. B)\(-\frac{11}{3} < x < 3\)
    3. C)\(x > 3\)
    4. D)\(x < -\frac{11}{3}\)
    Show answer

    Answer: \(x > 3\) or \(x < -\frac{11}{3}\)

    Hint: |3x + 1| > 10 means 3x + 1 > 10 or 3x + 1 < −10.

These are 9 of the 60 questions available for Inequalities. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.