Inequalities and Their Applications

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Q1. Which of the following values satisfies the inequality: 4 - x > 1?

Solution:

Step 1: Subtract 4 from both sides: -x > -3. Step 2: Multiply by -1 (reverse inequality): x < 3.

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Q2. Solve the inequality: -2(x + 3) > 4.

Solution:

Step 1: Distribute -2: -2x - 6 > 4. Step 2: Add 6: -2x > 10. Step 3: Divide by -2 (reverse inequality): x < -5.

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Q3. 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.

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Q4. 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).

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Q5. If 4x - 1 < 3x + 2, what is the value of x?

Solution:

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

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Q6. Solve the inequality: 7 - 3x ≥ 1.

Solution:

Step 1: Subtract 7 from both sides: -3x ≥ -6. Step 2: Divide by -3 (reverse inequality): x ≤ 2.

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Q7. If 3(x - 1) < 2x + 4, what is the value of x?

Solution:

Step 1: Distribute: 3x - 3 < 2x + 4. Step 2: Subtract 2x: x - 3 < 4. Step 3: Add 3: x < 7.

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Q8. Which of the following values satisfies the inequality: 3x + 4 < 10?

Solution:

Step 1: Subtract 4 from both sides: 3x < 6. Step 2: Divide by 3: x < 2.

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Q9. What is the solution to 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.

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Q10. 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).