Algebra Test Inequalities 2 — Questions and Answers
Question 1: Solve: 2x - 3 < 7
- x < 2
- x < 5 (Correct answer)
- x > 5
- x > 2
Correct answer: x < 5
Add 3 to both sides to get 2x < 10, then divide by 2 to get x < 5.
Question 2: What is the solution to -x ≥ 3?
- x ≥ -3
- x ≤ -3 (Correct answer)
- x ≥ 3
- x ≤ 3
Correct answer: x ≤ -3
Multiply both sides by -1 and flip: x ≤ -3.
Question 3: Solve the compound inequality: -1 < x + 2 < 5
- -3 < x < 3 (Correct answer)
- 1 < x < 7
- -3 < x < 7
- 1 < x < 3
Correct answer: -3 < x < 3
Subtract 2 from all three parts: -3 < x < 3.
Question 4: Which graph shows x ≤ -2?
- Open circle at -2, shading right
- Closed circle at -2, shading right
- Open circle at -2, shading left
- Closed circle at -2, shading left (Correct answer)
Correct answer: Closed circle at -2, shading left
x ≤ -2 uses a closed circle at -2 with shading to the left.
Question 5: Solve: 4x + 1 ≥ 2x + 9
- x ≥ 2
- x ≥ 4 (Correct answer)
- x ≤ 4
- x ≤ 2
Correct answer: x ≥ 4
Subtract 2x to get 2x + 1 ≥ 9, subtract 1 to get 2x ≥ 8, divide to get x ≥ 4.
Question 6: Which inequality represents 'x is between -3 and 6, exclusive'?
- -3 ≤ x ≤ 6
- -3 < x < 6 (Correct answer)
- -3 ≤ x < 6
- -3 < x ≤ 6
Correct answer: -3 < x < 6
'Exclusive' means the endpoints are not included, so strict inequalities are used.
Algebra Test Inequalities 2
Solve: 2x - 3 < 7