Linear inequalities might seem intimidating at first, especially when encountered in the expansive realm of mathematics. However, with a strong foundation and consistent practice, mastering them becomes a fulfilling journey. This article presents a set of multiple-choice questions tailored for Class 11 students to reinforce their understanding of linear inequalities. Let’s dive in!

## 1. If x > 5, then which of the following is also true?

### Answer:

### Explanation:

Multiplying both sides by 2, we get 2x > 10.

## 2. The solution to the inequality 3x – 4 > 5 is:

### Answer:

### Explanation:

Solving for x, 3x > 9 implies x > 3.

## 3. Which of the following inequalities is equivalent to x – 5 ≥ 7?

### Answer:

### Explanation:

Adding 5 to both sides, we get x ≥ 12.

## 4. The solution set for 2(x – 3) ≤ 4x – 6 is:

### Answer:

### Explanation:

Simplifying gives x ≤ 3.

## 5. If -2x < 8, then x is:

### Answer:

### Explanation:

Dividing both sides by -2 and reversing the inequality, we get x > -4.

## 6. Which of the following represents a valid inequality?

### Answer:

### Explanation:

Solving the inequality proves it to be valid.

## 7. The graph of the inequality x + 2y ≤ 6 will be:

### Answer:

### Explanation:

The inequality represents the region below the line x + 2y = 6.

## 8. For the inequality 2x + 3 > x + 7, x is:

### Answer:

### Explanation:

Solving for x, we get x > 4.

## 9. Which of the following is the solution to 4x – 7 > 2x + 5?

### Answer:

### Explanation:

Solving for x gives x > 3.

## 10. The solution for the inequality |x| < 3 is:

### Answer:

### Explanation:

The absolute value of x is less than 3 only if x is between -3 and 3.

## 11. Which inequality is represented by the number line with a closed circle at -2 and shading to the left?

### Answer:

### Explanation:

A closed circle indicates that the number is included, and shading to the left means values less than the number.

## 12. If 5 ≤ 2x – 3 < 11, then x lies between:

### Answer:

### Explanation:

Solving for x gives 4 ≤ x < 7.

## 13. The expression x^2 – 6x + 9 > 0 is true for:

### Answer:

### Explanation:

The expression is a perfect square, (x-3)^2, which is always non-negative.

## 14. For the inequality x/5 + 2 ≥ 3x/15 – 1, x is:

### Answer:

### Explanation:

Solving for x gives x ≤ 15.

## 15. Which inequality is equivalent to 2(x + 3) > x + 7?

### Answer:

### Explanation:

Expanding and solving for x gives x > 1.

## 16. The solution to the inequality x^2 – 4 > 0 is:

### Answer:

### Explanation:

Factoring gives (x-2)(x+2) > 0.

## 17. The inequality 5x – 3 < 2x + 6 is true when:

### Answer:

### Explanation:

Solving for x gives x > 3.

## 18. Which of the following is the solution set for the inequality 3x – 4 < 2x + 1?

### Answer:

### Explanation:

Solving for x gives x < 5.

## 19. The graph of the inequality 3x + 4y > 12 will shade:

### Answer:

### Explanation:

For this inequality, points above the line will satisfy the condition.

## 20. If 7x + 2 ≥ 5x + 12, then x is:

### Answer:

### Explanation:

Solving for x, we get x ≥ 5.