Grade: 9 Subject: Math (Algebra I) Unit: Linear Equations & Inequalities Lesson: 3 of 6 SAT: Algebra ACT: Math

Guided Practice

Learning Objectives

In this guided practice lesson, you will:

Work through these 10 problems. Click each question to reveal the answer and explanation.

Question 1: Solve for x: 3x + 7 = 22

Answer: x = 5

Solution: Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5. Check: 3(5) + 7 = 22.

Question 2: Solve for x: 2(x - 4) = 10

Answer: x = 9

Solution: Distribute: 2x - 8 = 10. Add 8: 2x = 18. Divide by 2: x = 9. Check: 2(9-4) = 2(5) = 10.

Question 3: Solve for x: 5x - 3 = 2x + 12

Answer: x = 5

Solution: Subtract 2x: 3x - 3 = 12. Add 3: 3x = 15. Divide by 3: x = 5. Check: 5(5)-3 = 22 and 2(5)+12 = 22.

Question 4: Solve for x: (x + 6)/2 = 8

Answer: x = 10

Solution: Multiply both sides by 2: x + 6 = 16. Subtract 6: x = 10. Check: (10+6)/2 = 16/2 = 8.

Question 5: Solve for x: 4(2x + 1) = 3(x - 2) + 25

Answer: x = 3

Solution: Distribute: 8x + 4 = 3x - 6 + 25. Simplify: 8x + 4 = 3x + 19. Subtract 3x: 5x + 4 = 19. Subtract 4: 5x = 15. Divide: x = 3.

Question 6: Solve for x: -2x + 9 = 3x - 6

Answer: x = 3

Solution: Add 2x: 9 = 5x - 6. Add 6: 15 = 5x. Divide by 5: x = 3. Check: -2(3)+9 = 3 and 3(3)-6 = 3.

Question 7: Solve for x: 7 - 3(x - 2) = 16

Answer: x = -1

Solution: Distribute: 7 - 3x + 6 = 16. Simplify: 13 - 3x = 16. Subtract 13: -3x = 3. Divide by -3: x = -1.

Question 8: Solve for x: 2x/3 + 5 = 11

Answer: x = 9

Solution: Subtract 5: 2x/3 = 6. Multiply by 3: 2x = 18. Divide by 2: x = 9. Check: 2(9)/3 + 5 = 6 + 5 = 11.

Question 9: Solve for x: 5(x + 2) - 3(x - 1) = 17

Answer: x = 2

Solution: Distribute: 5x + 10 - 3x + 3 = 17. Combine like terms: 2x + 13 = 17. Subtract 13: 2x = 4. Divide: x = 2.

Question 10: Solve for x: 3(2x - 5) = 4(x + 1) - 3

Answer: x = 8

Solution: Distribute: 6x - 15 = 4x + 4 - 3. Simplify: 6x - 15 = 4x + 1. Subtract 4x: 2x - 15 = 1. Add 15: 2x = 16. Divide: x = 8.