➕ Algebra 1 · Equations

Solving Multi-Step Equations practice questions

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Answer key with explanations

1. Solve 5(x − 2) = 35.

   Answer: x = 9. Distribute: 5x − 10 = 35. Add 10 to both sides: 5x = 45. Divide by 5: x = 9. Check: 5(9 − 2) = 35.

2. Solve 10x − 3x + 8 = 36.

   Answer: x = 4. Combine like terms: 7x + 8 = 36. Subtract 8 from both sides: 7x = 28. Divide by 7: x = 4. Check: 10(4) − 3(4) + 8 = 40 − 12 + 8 = 36.

3. Solve −3(x + 4) = 15.

   Answer: x = −9. Distribute −3: −3x − 12 = 15. Add 12 to both sides: −3x = 27. Divide both sides by −3: x = −9. Check: −3(−9 + 4) = −3(−5) = 15.

4. Solve 14 − (x − 3) = 6.

   Answer: x = 11. The minus flips both signs inside: 14 − x + 3 = 6, so 17 − x = 6. Subtract 17: −x = −11. Divide by −1: x = 11. Check: 14 − (11 − 3) = 14 − 8 = 6.

5. Solve 52 = 3(x − 4) + 5x.

   Answer: x = 8. Tidy the right side. Distribute: 3x − 12 + 5x. Combine like terms: 8x − 12. So 52 = 8x − 12. Add 12 to both sides: 64 = 8x. Divide by 8: x = 8. The variable is on the right, and the same steps work. Check: 3(8 − 4) + 5(8) = 12 + 40 = 52.

6. Solve x/3 + x/4 = 14.

   Answer: x = 24. The least common denominator is 12. Multiply every term by 12: 4x + 3x = 168. Combine: 7x = 168. Divide by 7: x = 24. Check: 24/3 + 24/4 = 8 + 6 = 14.

7. Solve (3/5)(x − 4) = 9.

   Answer: x = 19. Multiply both sides by the reciprocal 5/3: x − 4 = 15. Add 4 to both sides: x = 19. Check: (3/5)(19 − 4) = (3/5)(15) = 9.

8. A kayak rental charges h dollars per hour plus a 2-dollar life-jacket fee for each hour. There is also a one-time 6-dollar launch fee. Sam rents a kayak for 4 hours and pays 46 dollars in total. What is the hourly price h?

   Answer: 8 dollars per hour. Each hour costs h + 2, so the total is 4(h + 2) + 6 = 46. Distribute: 4h + 8 + 6 = 46, so 4h + 14 = 46. Subtract 14: 4h = 32. Divide by 4: h = 8. Check: 4(8 + 2) + 6 = 46.