Practice: Linear Equations

Part A: Two-Step Equations

Directions: Solve each equation. Show your work and check your answer.

1. 3x + 7 = 22

x =

2. 5x - 9 = 31

x =

3. 2x + 15 = 3

x =

4. 4x - 7 = -19

x =

Part B: Equations with Distributive Property

Directions: Distribute first, then solve. Show all steps.

5. 2(x + 5) = 18

x =

6. 3(x - 4) = 15

x =

7. 5(2x + 1) = 35

x =

8. 4(x - 2) + 3 = 19

x =

Part C: Variables on Both Sides

Directions: Move all variables to one side, then solve.

9. 7x + 3 = 4x + 18

x =

10. 9x - 5 = 6x + 10

x =

11. 2x + 14 = 5x - 1

x =

12. 8x - 12 = 3x + 8

x =

Part D: Identifying Special Cases

Directions: Solve each equation. Identify if it has one solution, no solution, or infinite solutions.

13. 3x + 6 = 3x + 6

Solution type: ______________ (One solution / No solution / Infinite solutions)

14. 2x + 5 = 2x + 9

Solution type: ______________ (One solution / No solution / Infinite solutions)

15. 4(x + 2) = 4x + 8

Solution type: ______________ (One solution / No solution / Infinite solutions)

16. 6x - 3 = 3(2x + 1)

Solution type: ______________ (One solution / No solution / Infinite solutions)

Part E: Word Problems

Directions: Write an equation and solve.

17. Sarah has $45 and saves $12 per week. Her brother has $93 and spends $6 per week. After how many weeks will they have the same amount?

Let x = number of weeks

Equation: _________________ Answer: _______ weeks

18. A phone plan charges $25 per month plus $0.10 per text. Another plan charges $15 per month plus $0.15 per text. For how many texts are the costs equal?

Equation: _________________ Answer: _______ texts

19. The perimeter of a rectangle is 48 cm. The length is 3 more than twice the width. Find the dimensions.

Width: _______ cm Length: _______ cm

Challenge: Think About It!

20. Solve: 3(2x - 4) - 2(x + 5) = 2(x - 11)

x = _______ OR Solution type: _____________

21. Create your own equation that has NO SOLUTION. Then show why it has no solution.