MCQs / Mathematics / Linear Equations and Inequalities

Linear Equations and Inequalities MCQs — Mathematics

45 multiple-choice questions on Linear Equations and Inequalities from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

1. The solution set of -3 < 2x + 1 le 7 is:

  1. -2 < x le 3
  2. -1 < x le 4
  3. -2 < x le 4
  4. -2 le x < 3

Answer: A) -2 < x le 3

Explanation: Subtract 1: -4 < 2x le 6; divide by 2: -2 < x le 3. SLO M-09-A-22 · Understanding

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2. Which point satisfies both y le 2x and x + y 3?

  1. (5, -2)
  2. (-3, -1)
  3. (6, 0)
  4. (2, 5)

Answer: C) (6, 0)

Explanation: Substitute (6, 0): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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3. Solve 43x + 16 = 56.

  1. x = 34
  2. x = - 12
  3. x = 12
  4. x = 58

Answer: C) x = 12

Explanation: 43x = 56 - 16 = 23, so x = 23 div 43 = 12. SLO M-09-A-22 · Understanding

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4. Solve 4(x + 1) = 6x - 3.

  1. x = 72
  2. x = 112
  3. x = - 12
  4. x = - 72

Answer: A) x = 72

Explanation: 4x + 4 = 6x - 3 Rightarrow -2x = -7 Rightarrow x = 72. SLO M-09-A-22 · Understanding

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5. Solve 5(x + 4) = 3x - 2.

  1. x = -11
  2. x = 9
  3. x = 11
  4. x = -9

Answer: A) x = -11

Explanation: 5x + 20 = 3x - 2 Rightarrow 2x = -22 Rightarrow x = -11. SLO M-09-A-22 · Understanding

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6. The boundary lines 2x + y = 8 and x - y = 1 meet at the corner point:

  1. (-3, 2)
  2. (4, 1)
  3. (2, 3)
  4. (3, 2)

Answer: D) (3, 2)

Explanation: Solving the two equations together gives x = 3, y = 2. SLO M-10-A-23 · Understanding

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7. Solve -5x + 3 le -12.

  1. x ge -3
  2. x le 3
  3. x le -3
  4. x ge 3

Answer: D) x ge 3

Explanation: -5x le -15. Dividing by -5 reverses the sign because it is negative: x ge 3. SLO M-09-A-22 · Understanding

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8. Which point satisfies both y x - 3 and x + y le 5?

  1. (4, 6)
  2. (3, -1)
  3. (5, 6)
  4. (-3, -3)

Answer: D) (-3, -3)

Explanation: Substitute (-3, -3): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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9. Solve 15x - 12 = 32.

  1. x = 152
  2. x = 10
  3. x = -10
  4. x = 5

Answer: B) x = 10

Explanation: 15x = 32 + 12 = 2, so x = 2 div 15 = 10. SLO M-09-A-22 · Understanding

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10. Solve 3(x - 2) = 2x + 5.

  1. x = 11
  2. x = -1
  3. x = -11
  4. x = 13

Answer: A) x = 11

Explanation: 3x - 6 = 2x + 5 Rightarrow 1x = 11 Rightarrow x = 11. SLO M-09-A-22 · Understanding

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11. Which point satisfies both 2x + y < 8 and y ge 1?

  1. (5, -2)
  2. (0, 2)
  3. (5, 4)
  4. (4, 5)

Answer: B) (0, 2)

Explanation: Substitute (0, 2): it makes both inequalities true. Each other point fails at least one of them. SLO M-10-A-23 · Understanding

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12. Solve 56x - 23 = 133.

  1. x = -6
  2. x = 6
  3. x = 225
  4. x = 265

Answer: B) x = 6

Explanation: 56x = 133 + 23 = 5, so x = 5 div 56 = 6. SLO M-09-A-22 · Understanding

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13. Which point is not in the solution region of 2x + y < 8 and y ge 1?

  1. (-2, -3)
  2. (-2, 6)
  3. (-1, 2)
  4. (0, 6)

Answer: A) (-2, -3)

Explanation: (-2, -3) fails at least one of the inequalities; the other points satisfy both. SLO M-10-A-23 · Understanding

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14. When graphing y ge -x + 3, the boundary line is drawn:

  1. solid, and the region below it is shaded
  2. dashed, and the region below it is shaded
  3. solid, and the region above it is shaded
  4. dashed, and the region above it is shaded

Answer: C) solid, and the region above it is shaded

Explanation: ge includes the line (solid), and y ge means the region above the line. SLO M-10-A-23 · Understanding

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15. Solve 4x + 7 -9.

  1. x -4
  2. x < -4
  3. x 4
  4. x < 4

Answer: A) x -4

Explanation: 4x -16. Dividing by 4 keeps the sign: x -4. SLO M-09-A-22 · Understanding

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16. Solve x - 13 le x4.

  1. x le 4
  2. x le 12
  3. x ge 4
  4. x le -4

Answer: A) x le 4

Explanation: Multiply by 12: 4(x - 1) le 3x Rightarrow 4x - 4 le 3x Rightarrow x le 4. SLO M-09-A-22 · Understanding

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17. Solve 34x + 52 = - 12.

  1. x = 83
  2. x = - 23
  3. x = -4
  4. x = 4

Answer: C) x = -4

Explanation: 34x = - 12 - 52 = -3, so x = -3 div 34 = -4. SLO M-09-A-22 · Understanding

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18. Is the point (2, 1) in the solution region of x + y 3 and y < 2?

  1. Yes, it satisfies both
  2. No, because x + y = 3 is not greater than 3
  3. Yes, because x y
  4. No, because y < 2 fails

Answer: B) No, because x + y = 3 is not greater than 3

Explanation: 2 + 1 = 3, and 3 3 is false; points on a dashed boundary line are not included. SLO M-10-A-23 · Understanding

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19. With 20x + 50y le 300 and y ge 2 (x pens, y notebooks), which purchase is possible?

  1. x = 15, y = 1
  2. x = 5, y = 5
  3. x = 10, y = 2
  4. x = 12, y = 2

Answer: C) x = 10, y = 2

Explanation: 20(10) + 50(2) = 300 le 300 and y = 2 ge 2. The others cost too much or have too few notebooks. SLO M-10-A-23 · Understanding

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20. A number line shows a closed circle at -1, a closed circle at 4 and the segment between them shaded. Which inequality does it represent?

  1. -1 le x < 4
  2. -1 < x < 4
  3. -1 le x le 4
  4. x le -1 or x ge 4

Answer: C) -1 le x le 4

Explanation: An open circle means the end point is not included (< or ); a closed circle means it is included (le or ge). SLO M-09-A-22 · Understanding

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21. The solution region of x + y le 5 contains the origin because:

  1. 0 + 0 = 5
  2. 0 + 0 5
  3. the line passes through the origin
  4. 0 + 0 le 5

Answer: D) 0 + 0 le 5

Explanation: Test (0, 0): 0 le 5 is true, so the origin's side is shaded. SLO M-10-A-23 · Understanding

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22. Which system describes the strip between the lines y = 1 and y = 4, including both lines?

  1. y ge 1 and y le 4
  2. y 1 and y < 4
  3. x ge 1 and x le 4
  4. y le 1 and y ge 4

Answer: A) y ge 1 and y le 4

Explanation: Between the lines means above y = 1 and below y = 4; including the lines uses ge and le. SLO M-10-A-23 · Understanding

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23. Which point is not in the solution region of x + 2y ge 4 and x - y < 1?

  1. (4, 3)
  2. (2, 4)
  3. (1, 4)
  4. (1, 6)

Answer: A) (4, 3)

Explanation: (4, 3) fails at least one of the inequalities; the other points satisfy both. SLO M-10-A-23 · Understanding

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24. Solve -2x + 5 < 11.

  1. x < 3
  2. x -3
  3. x < -3
  4. x 3

Answer: B) x -3

Explanation: -2x < 6. Dividing by -2 reverses the sign because it is negative: x -3. SLO M-09-A-22 · Understanding

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25. The corner points of the region x ge 0, y ge 0, x + y le 4 are:

  1. (0, 0), (4, 0), (4, 4)
  2. (0, 0), (4, 0), (0, 4)
  3. (0, 0), (2, 2), (4, 4)
  4. (4, 0), (0, 4), (4, 4)

Answer: B) (0, 0), (4, 0), (0, 4)

Explanation: The line x + y = 4 cuts the axes at (4, 0) and (0, 4); together with the origin these form a triangle. SLO M-10-A-23 · Understanding

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