LINEAR INEQUALITIES

Linear Inequalities)

1. Solve the inequality: 3x − 5 > 7. The solution set is:
   1. x ≥ 4
   2. x > −4
   3. x > 4
   4. x ≥ 5
2. Solve the inequality: −2 ≤ 3x + 1 < 7. The solution set is:
   1. −1 ≤ x < 2
   2. x > −1
   3. x < 2
   4. −2 < x ≤ 7
3. Which inequality correctly represents the statement:
   “Twice a number reduced by 3 is at most 11”?
   1. 2x − 3 ≥ 11
   2. 2x − 3 > 11
   3. 2x − 3 ≤ 11
   4. 2x + 3 ≤ 11
4. Solve the inequality: −2x + 7 ≥ 1.
   1. x ≥ 3
   2. x ≤ 3
   3. x > −3
   4. x < −3
5. Find the common solution set of the inequalities:
   2x − 1 > 5 and x + 3 ≤ 10.
   1. 3 < x ≤ 7
   2. x > 7
   3. x ≤ 3
   4. −3 ≤ x ≤ 10
6. Solve the inequality: x − 4 < 3. In set-builder notation, the solution set is:
   1. { x ∈ ℝ : x > 7 }
   2. { x ∈ ℝ : x < 7 }
   3. { x ∈ ℝ : x ≥ 7 }
   4. { x ∈ ℝ : x ≤ 7 }
7. In an exam of 50 marks, a student must score at least 40% to pass. If x represents the student’s score, which inequality represents this condition?
   1. x > 40
   2. x ≥ 40
   3. x ≥ 20
   4. x ≤ 20
8. Solve the inequality: x/3 − 2 ≤ 1/3.
   1. x ≤ 7
   2. x ≥ 7
   3. x < 7
   4. x > 7
9. A region in the xy-plane is described as the set of all points (x, y) that lie on or above the line y = 2x + 3. Which inequality represents this region?
   1. y > 2x + 3
   2. y < 2x + 3
   3. y ≤ 2x + 3
   4. y ≥ 2x + 3
10. To subscribe to a certain data bundle, a customer must recharge at least ₦500 but not more than ₦2000. If x represents the amount recharged (in naira), which inequality best represents this condition?
    1. x > 500
    2. x ≥ 500 and x < 2000
    3. 500 ≤ x ≤ 2000
    4. x > 2000

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