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Grade 10 · Exponents, Equations and Inequalities
Linear Inequalities & Interval Notation (Grade 10)
MEMORANDUM
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Mark
  / 15

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Solve: 2x + 3 < 11
    (2)
    2x < 8 → x < 4, i.e. (−∞ ; 4)✓✓ (2)
  2. 2
    Solve: 5x − 4 ≥ 16
    (2)
    5x ≥ 20 → x ≥ 4, i.e. [4 ; ∞)✓✓ (2)
  3. 3
    Solve: −2x > 10
    (2)
    x < −5 (sign flips), i.e. (−∞ ; −5)✓✓ (2)
  4. 4
    Solve: −3x + 1 ≤ 7
    (2)
    −3x ≤ 6 → x ≥ −2, i.e. [−2 ; ∞)✓✓ (2)
  5. 5
    Write x > 5 in interval notation.
    (1)
    (5 ; ∞)✓ (1)
  6. 6
    Write −2 ≤ x ≤ 7 in interval notation.
    (1)
    [−2 ; 7]✓ (1)
  7. 7
    Write (−∞ ; 3] as an inequality.
    (1)
    x ≤ 3✓ (1)
  8. 8
    Solve: −4 < 2x − 2 ≤ 6
    (3)
    −1 < x ≤ 4 → (−1 ; 4]✓✓✓ (3)
  9. 9
    On a number line, what does an OPEN circle mean?
    (1)
    −10123456x > 2−10123456x ≥ 2
    The value is not included (< or >).✓ (1)
TOTAL: 15 marks
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