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Q1. What is the simplified form of the expression (x^2 - 1)/(x - 1)?
Solution:
Step 1: Factor the numerator: (x - 1)(x + 1)/(x - 1). Step 2: Cancel (x - 1): x + 1.
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Q2. What is the solution to the equation 4x - 1 = 3x + 2?
Solution:
Step 1: Subtract 3x from both sides: x - 1 = 2. Step 2: Add 1 to both sides: x = 3.
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Q3. What is the simplified form of the expression 3(x + 2) - 2(x - 1)?
Solution:
Step 1: Distribute: 3x + 6 - 2x + 2. Step 2: Combine like terms: (3x - 2x) + (6 + 2) = x + 8.
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Q4. Which of the following represents the solution set for the inequality 2x + 5 > 3?
Solution:
Step 1: Subtract 5 from both sides: 2x > -2. Step 2: Divide by 2: x > -1.
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Q5. Solve for x: 5(x - 1) = 3x + 7.
Solution:
Step 1: Distribute: 5x - 5 = 3x + 7. Step 2: Subtract 3x from both sides: 2x - 5 = 7. Step 3: Add 5 to both sides: 2x = 12. Step 4: Divide by 2: x = 6.
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Q6. What is the product of the roots of the quadratic equation x^2 + 6x + 8 = 0?
Solution:
Step 1: Use the formula c/a. Step 2: Here, c = 8 and a = 1. Step 3: Product of roots = 8.
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Q7. What is the value of x in the inequality 3x - 4 < 5?
Solution:
Step 1: Add 4 to both sides: 3x < 9. Step 2: Divide both sides by 3: x < 3.
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Q8. What is the solution to the equation 4x - 7 = 5x + 2?
Solution:
Step 1: Subtract 4x from both sides: -7 = x + 2. Step 2: Subtract 2 from both sides: -9 = x. Step 3: x = -9.
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Q9. What is the simplified form of the expression 3x^2 - 2x + 4x^2 - 5?
Solution:
Step 1: Combine like terms: (3x^2 + 4x^2) + (-2x) - 5 = 7x^2 - 5.
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Q10. Which of the following represents the solution set for the inequality 2x + 3 > 7?
Solution:
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
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