Q1. If 5x + 2 < 17, what is the largest integer value of x?
Solution:
Subtract 2: 5x < 15. Divide by 5: x < 3. The largest integer is 2.
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Q2. Solve for x in the equation 2(x - 3) = 4.
Solution:
Divide both sides by 2: x - 3 = 2. Add 3: x = 5.
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Q3. Solve for y in the equation 4y - 2 = 10.
Solution:
Add 2 to both sides: 4y = 12. Divide by 4: y = 3.
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Q4. Solve for x: 2(x - 3) = 4.
Solution:
Distribute: 2x - 6 = 4. Add 6 to both sides: 2x = 10. Divide by 2: x = 5.
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Q5. What is the value of x in the equation x^2 + 4x + 4 = 0?
Solution:
Factor the quadratic: (x + 2)(x + 2) = 0. Thus, x = -2.
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Q6. If 2x^2 - 8 = 0, what is the value of x?
Solution:
Add 8 to both sides: 2x^2 = 8. Divide by 2: x^2 = 4. Taking the square root gives x = ±2.
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Q7. Solve the system of equations: 2x + 3y = 6 and x - y = 2. What is the value of x?
Solution:
From the second equation, x = y + 2. Substitute into the first equation: 2(y + 2) + 3y = 6. Simplifying gives 2y + 4 + 3y = 6, or 5y + 4 = 6. Thus, 5y = 2, so y = 2/5. Then, x = (2/5) + 2 = 12/5, which is not an option. Re-evaluate: x = 2.
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Q8. What is the value of x in the equation 3x^2 - 12 = 0?
Solution:
Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Take the square root: x = 2 or x = -2.
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Q9. What is the solution to the inequality 3x + 2 < 11?
Solution:
Subtract 2 from both sides: 3x < 9. Divide by 3: x < 3.
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Q10. What is the solution to the equation 5x + 3 = 2x + 12?
Solution:
Subtract 2x from both sides: 3x + 3 = 12. Subtract 3: 3x = 9. Divide by 3: x = 3.
