Inequalities and Their Applications

⏱ Time: 0s

Q1. Which of the following values satisfies the inequality: 4x - 1 < 3x + 2?

Solution:

Step 1: Subtract 3x from both sides: x - 1 < 2. Step 2: Add 1: x < 3.

⏱ Time: 0s

Q2. Solve the inequality: -2(x + 3) > 6.

Solution:

Step 1: Distribute: -2x - 6 > 6. Step 2: Add 6: -2x > 12. Step 3: Divide by -2 (reverse inequality): x < -6.

⏱ Time: 0s

Q3. What is the solution set for the inequality: x^2 - 4 < 0?

Solution:

Step 1: Factor: (x - 2)(x + 2) < 0. Step 2: Test intervals: solution is (-2, 2).

⏱ Time: 0s

Q4. If 2x + 3 > 11, what is the solution for x?

Solution:

Step 1: Subtract 3 from both sides: 2x > 8. Step 2: Divide by 2: x > 4.

⏱ Time: 0s

Q5. Solve the inequality: 7x + 1 ≤ 3x + 9.

Solution:

Step 1: Subtract 3x from both sides: 4x + 1 ≤ 9. Step 2: Subtract 1: 4x ≤ 8. Step 3: Divide by 4: x ≤ 2.

⏱ Time: 0s

Q6. Solve the inequality: x^2 - 5x + 6 > 0.

Solution:

Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (-∞, 2) ∪ (3, ∞).

⏱ Time: 0s

Q7. What is the solution to the inequality: 2(x - 1) < 3(x + 2)?

Solution:

Step 1: Distribute: 2x - 2 < 3x + 6. Step 2: Subtract 2x: -2 < x + 6. Step 3: Subtract 6: -8 < x, or x > -8.

⏱ Time: 0s

Q8. Solve the inequality: x^2 - 9 > 0.

Solution:

Step 1: Factor: (x - 3)(x + 3) > 0. Step 2: Test intervals: solution is x < -3 or x > 3.

⏱ Time: 0s

Q9. Which of the following represents the solution to the inequality: x^2 - 5x + 6 > 0?

Solution:

Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (3, ∞) ∪ (-∞, 2).

⏱ Time: 0s

Q10. Solve the inequality: 7 - 2x ≥ 3.

Solution:

Step 1: Subtract 7 from both sides: -2x ≥ -4. Step 2: Divide by -2 (reverse inequality): x ≤ 2.