Linear Equations in One Variable

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Q1. What is the value of x in the equation 4x^2 - 12x = 0?

Solution:

Factor: 4x(x - 3) = 0. So, x = 0 or x = 3.

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Q2. Solve for x: 7 - 2x = 1

Solution:

Subtract 7 from both sides: -2x = -6. Divide by -2: x = 3.

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Q3. Solve the inequality: 2x - 5 < 3

Solution:

Add 5 to both sides: 2x < 8. Divide by 2: x < 4.

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Q4. What is the value of x in the equation 7x + 2 = 23?

Solution:

Subtract 2: 7x = 21. Divide by 7: x = 3.

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Q5. Solve for x: x/4 - 2 = 1

Solution:

Add 2 to both sides: x/4 = 3. Multiply by 4: x = 12.

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Q6. Solve for x: 3(x + 2) = 21

Solution:

Divide by 3: x + 2 = 7. Subtract 2: x = 5.

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Q7. Solve for x: x/4 + 5 = 9

Solution:

Subtract 5 from both sides: x/4 = 4. Multiply by 4: x = 16.

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Q8. What is the solution to the equation x^2 - 9 = 0?

Solution:

Factor: (x - 3)(x + 3) = 0. Solutions are x = 3 and x = -3.

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Q9. If 2(x + 3) = 10, what is x?

Solution:

Divide by 2: x + 3 = 5. Subtract 3: x = 2.

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Q10. If 2(x + 3) = 16, what is x?

Solution:

Divide by 2: x + 3 = 8. Subtract 3: x = 5.