science Olympiad

medium calculas problem with linear equations in one variable

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1. Solve for x: 3x - 7 = 14

Solution
Correct: A
Add 7 to both sides: 3x = 21. Divide by 3: x = 21 ÷ 3 = 7.

2. If 5x + 2 = 3x + 10, what is x?

Solution
Correct: A
Subtract 3x: 2x + 2 = 10. Subtract 2: 2x = 8. Divide by 2: x = 4.

3. Find x when 2(x + 4) = 18

Solution
Correct: B
Divide by 2: x + 4 = 9. Subtract 4: x = 5.

4. Solve: 4x - 5 = 2x + 11

Solution
Correct: A
Subtract 2x: 2x - 5 = 11. Add 5: 2x = 16. Divide: x = 8.

5. What is x if 7x + 3 = 5x + 15?

Solution
Correct: A
Subtract 5x: 2x + 3 = 15. Subtract 3: 2x = 12. Divide: x = 6.

6. Solve for x: 3(x - 2) = 2x + 5

Solution
Correct: A
Expand: 3x - 6 = 2x + 5. Subtract 2x: x - 6 = 5. Add 6: x = 11.

7. If 9 - 2x = x + 3, find x.

Solution
Correct: A
Add 2x: 9 = 3x + 3. Subtract 3: 6 = 3x. Divide: x = 2.

8. Find x: 5x + 4 = 3x + 12

Solution
Correct: A
Subtract 3x: 2x + 4 = 12. Subtract 4: 2x = 8. Divide: x = 4.

9. Solve: 2x - 9 = x + 4

Solution
Correct: A
Subtract x: x - 9 = 4. Add 9: x = 13.

10. What is x if 6x - 8 = 22?

Solution
Correct: A
Add 8: 6x = 30. Divide: x = 5.

11. Solve for x: 4(x + 1) = 3x + 10

Solution
Correct: A
Expand: 4x + 4 = 3x + 10. Subtract 3x: x + 4 = 10. Subtract 4: x = 6.

12. If 8x - 5 = 2x + 13, find x.

Solution
Correct: A
Subtract 2x: 6x - 5 = 13. Add 5: 6x = 18. Divide: x = 3.

13. Find x: 5 - 3x = 2x + 15

Solution
Correct: A
Add 3x: 5 = 5x + 15. Subtract 15: -10 = 5x. Divide: x = -2.

14. Solve: 7x + 6 = 4x + 18

Solution
Correct: A
Subtract 4x: 3x + 6 = 18. Subtract 6: 3x = 12. Divide: x = 4.

15. What is x when 3x - 4 = x + 8?

Solution
Correct: A
Subtract x: 2x - 4 = 8. Add 4: 2x = 12. Divide: x = 6.

16. Solve for x: 2(3x - 1) = 16

Solution
Correct: A
Divide by 2: 3x - 1 = 8. Add 1: 3x = 9. Divide: x = 3.

17. If 10x - 7 = 3x + 14, find x.

Solution
Correct: A
Subtract 3x: 7x - 7 = 14. Add 7: 7x = 21. Divide: x = 3.

18. Find x: 4x + 9 = 2x + 17

Solution
Correct: A
Subtract 2x: 2x + 9 = 17. Subtract 9: 2x = 8. Divide: x = 4.

19. Solve: 6x - 5 = x + 20

Solution
Correct: A
Subtract x: 5x - 5 = 20. Add 5: 5x = 25. Divide: x = 5.

20. What is x if 2x + 7 = 19?

Solution
Correct: A
Subtract 7: 2x = 12. Divide: x = 6.

21. Solve for x: 5(x - 3) = 2x + 6

Solution
Correct: A
Expand: 5x - 15 = 2x + 6. Subtract 2x: 3x - 15 = 6. Add 15: 3x = 21. Divide: x = 7.

22. If 11x - 9 = 5x + 15, find x.

Solution
Correct: A
Subtract 5x: 6x - 9 = 15. Add 9: 6x = 24. Divide: x = 4.

23. Find x: 3x + 8 = x + 16

Solution
Correct: A
Subtract x: 2x + 8 = 16. Subtract 8: 2x = 8. Divide: x = 4.

24. Solve: 9x - 4 = 5x + 12

Solution
Correct: A
Subtract 5x: 4x - 4 = 12. Add 4: 4x = 16. Divide: x = 4.

25. What is x when 4x - 6 = 2x + 10?

Solution
Correct: A
Subtract 2x: 2x - 6 = 10. Add 6: 2x = 16. Divide: x = 8.

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