Q1. What is the solution to the inequality: 2x^2 - 8 < 0?
Solution:
Step 1: Factor: 2(x^2 - 4) < 0. Step 2: Further factor: 2(x - 2)(x + 2) < 0. Step 3: The solution is (-2, 2).
⏱ Time: 0s
Q2. Which of the following is a solution to the inequality: x^2 - 4x < 0?
Solution:
Step 1: Factor the inequality: x(x - 4) < 0. Step 2: The critical points are x = 0 and x = 4. Step 3: Test intervals: (0, 4) is valid.
⏱ Time: 0s
Q3. Find the solution set for the inequality: 4x - 7 ≤ 9.
Solution:
Step 1: Add 7 to both sides: 4x ≤ 16. Step 2: Divide by 4: x ≤ 4.
⏱ Time: 0s
Q4. What is the solution to the inequality: 5 - 2x > 3?
Solution:
Step 1: Subtract 5 from both sides: -2x > -2. Step 2: Divide by -2 (reverse inequality): x < 1.
⏱ Time: 0s
Q5. Solve the inequality: 6 - 3x < 0.
Solution:
Step 1: Subtract 6 from both sides: -3x < -6. Step 2: Divide by -3 (reverse inequality): x > 2.
⏱ Time: 0s
Q6. Determine the solution set for the inequality: 2x^2 - 8 < 0.
Solution:
Step 1: Factor the inequality: 2(x^2 - 4) < 0. Step 2: Roots are x = -2 and x = 2. Step 3: The solution is between the roots: (-2, 2).
⏱ Time: 0s
Q7. What is the solution to the inequality: -3x + 6 ≤ 0?
Solution:
Step 1: Subtract 6 from both sides: -3x ≤ -6. Step 2: Divide by -3 (reverse the inequality): x ≥ 2.
⏱ Time: 0s
Q8. Find the solution to the inequality: x^2 - 9 > 0.
Solution:
Step 1: Factor the inequality: (x - 3)(x + 3) > 0. Step 2: The critical points are x = -3 and x = 3. Step 3: Test intervals: The solution set is (-∞, -3) ∪ (3, ∞).
⏱ Time: 0s
Q9. Determine the solution set for the inequality: x^2 - 6x + 8 ≤ 0.
Solution:
Step 1: Factor: (x - 2)(x - 4) ≤ 0. Step 2: The solution is between the roots: [2, 4].
⏱ Time: 0s
Q10. Determine the solution for the inequality: 3(x - 1) < 2(x + 2).
