Simultaneous Linear Equations

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Q1. 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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Q2. What is the value of x in the equation 7x - 2 = 5x + 6?

Solution:

Subtract 5x from both sides: 2x - 2 = 6. Add 2 to both sides: 2x = 8. Divide by 2: x = 4.

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Q3. 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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Q4. 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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Q5. If 4x + 5 = 29, what is the value of x?

Solution:

Subtract 5 from both sides: 4x = 24. Divide by 4: x = 6.

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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 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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Q8. 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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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. Solve for y in the equation 2y - 3 = 7.

Solution:

Add 3 to both sides: 2y = 10. Divide by 2: y = 5.