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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Q2. What is the solution to the quadratic equation x^2 - 5x + 6 = 0?
Solution:
Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.
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Q3. Solve for y in the equation 2y - 3 = 7.
Solution:
Add 3 to both sides: 2y = 10. Divide by 2: y = 5.
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Q4. Solve the system of equations: 2x + 3y = 6 and x - y = 1. What is the value of x?
Solution:
From the second equation, x = y + 1. Substitute into the first equation: 2(y + 1) + 3y = 6. Simplifying gives 2y + 2 + 3y = 6, or 5y + 2 = 6. Thus, 5y = 4, so y = 0.8. Therefore, x = 0.8 + 1 = 1.8.
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Q5. If 6x - 3 = 3x + 12, what is the value of x?
Solution:
Subtract 3x from both sides: 3x - 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5.
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Q6. Solve for x in the equation 7x + 2 = 23.
Solution:
Subtract 2 from both sides: 7x = 21. Divide by 7: x = 3.
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Q7. 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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Q8. What is the solution to the inequality 5x - 2 < 3?
Solution:
Add 2 to both sides: 5x < 5. Divide by 5: x < 1.
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Q9. 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.
