Linear Inequalities

Q. If -2x + 4 > 0, what is the range of x?

Solution

-2x > -4 => x < 2. The range is x < 2.

Correct Answer: A — x < 2

Q. If 3x + 5 < 20, what is the maximum integer value of x?

Solution

3x < 15 => x < 5. The maximum integer value is 5.

Correct Answer: B — 5

Q. If 7x - 2 ≤ 5, what is the maximum integer value of x?

Solution

7x ≤ 7 => x ≤ 1. The maximum integer value is 1.

Correct Answer: B — 1

Q. If 8 - 3x ≥ 2, what is the minimum integer value of x?

Solution

-3x ≥ -6 => x ≤ 2. The minimum integer value is 2.

Correct Answer: B — 2

Q. Solve the inequality: 2x - 3 > 7.

Solution

2x > 10 => x > 5. The smallest integer satisfying this is 6.

Correct Answer: C — 5

Q. Solve the inequality: 6 - 2x < 4.

Solution

-2x < -2 => x > 1. The solution is x > 1.

Correct Answer: A — x > 1

Q. What is the solution set for the inequality: 5 - x < 3?

Solution

-x < -2 => x > 2. The solution set is x > 2.

Correct Answer: A — x > 2

Q. Which of the following is a solution to the inequality: 3x + 4 > 10?

Solution

3x > 6 => x > 2. The value 3 satisfies the inequality.

Correct Answer: B — 2

Q. Which of the following values satisfies the inequality: 4x + 1 ≤ 13?

Solution

4x ≤ 12 => x ≤ 3. The value 3 satisfies the inequality.

Correct Answer: B — 3

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