Linear Equations in One Variable

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Q1. A number is divided by 2 and then increased by 6 to get 10. What is the number?

Solution:

Let the number be x. The equation is (x / 2) + 6 = 10. Subtracting 6 from both sides gives x / 2 = 4. Multiplying by 2 gives x = 8.

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Q2. The difference between a number and 9 is 5. What is the number?

Solution:

Let the number be x. The equation is x - 9 = 5. Adding 9 gives x = 14.

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Q3. If 5 times a number is decreased by 2, the result is 18. What is the number?

Solution:

Let the number be x. Then, 5x - 2 = 18. Adding 2 to both sides gives 5x = 20. Dividing by 5 gives x = 4.

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Q4. A number decreased by 7 is equal to 3. What is the number?

Solution:

Let the number be x. The equation is x - 7 = 3. Adding 7 to both sides gives x = 10.

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Q5. Twice a number decreased by 5 equals 11. What is the number?

Solution:

Let the number be x. The equation is 2x - 5 = 11. Adding 5 to both sides gives 2x = 16. Dividing by 2 gives x = 8.

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Q6. If a number is multiplied by 6 and then decreased by 4, the result is 14. What is the number?

Solution:

Let the number be x. The equation is 6x - 4 = 14. Adding 4 gives 6x = 18, so x = 3.

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Q7. A number is divided by 2 and then increased by 3. The result is 10. What is the number?

Solution:

Let the number be x. Then, x/2 + 3 = 10. Subtracting 3 from both sides gives x/2 = 7. Multiplying by 2 gives x = 14.

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Q8. A number is subtracted from 15 and the result is 9. What is the number?

Solution:

Let the number be x. The equation is 15 - x = 9. Subtracting 15 from both sides gives -x = -6. Multiplying by -1 gives x = 6.

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Q9. A number is tripled and then increased by 2 to equal 20. What is the number?

Solution:

Let the number be x. The equation is 3x + 2 = 20. Subtracting 2 gives 3x = 18, so x = 6.

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Q10. If 4 times a number is increased by 6, the result is 30. What is the number?

Solution:

Let the number be x. Then, 4x + 6 = 30. Subtracting 6 from both sides gives 4x = 24. Dividing by 4 gives x = 6.