A free printable worksheet that pairs with the Tip the Scales game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Solving Equations

Grades 6–8 · CCSS 6.EE.B.7, 7.EE.B.4a, 8.EE.C.7b · Pairs with the Tip the Scales game

Name

Date

An equation is a balance: both sides are equal. Whatever you do to one side, do to the other. Use inverse operations to get x alone: undo adding by subtracting, and undo multiplying by dividing. Check your answer by substituting it back in.

Key vocabulary

equation: a statement that two expressions are equal, like 2x + 3 = 11
variable: a letter, like x, that stands for an unknown number
coefficient: the number multiplied by the variable; in 2x, the coefficient is 2
constant: a number on its own, without a variable
solution: the value of the variable that makes the equation true
inverse operations: operations that undo each other: add and subtract, multiply and divide
like terms: terms with the same variable part, like 3x and 5x, which can be combined
distributive property: a(b + c) = ab + ac, as in 2(x + 4) = 2x + 8

Part A: One-step equations

1. x + 3 = 8

x =

2. x − 4 = 9

x =

3. 4x = 28

x =

4. x / 5 = 6

x =

Part B: Two-step equations

5. 2x + 1 = 7

x =

6. 3x − 5 = 16

x =

7. 5x + 4 = 29

x =

8. x / 2 + 3 = 10

x =

Part C: Variables on both sides

9. 3x + 2 = x + 8

x =

10. 5x − 4 = 2x + 11

x =

11. 7x + 3 = 4x + 18

x =

12. 6x = 2x + 20

x =

Part D: The distributive property (expand first, or divide first)

13. 2(x + 1) = 4

x =

14. 3(x − 2) = 15

x =

15. 4(x + 3) = 2x + 20

x =

16. 5(x + 1) = 3(x + 3)

x =

Part E: Apply it

17. Gym A costs $30 to join plus $10 a month. Gym B costs $15 a month with no fee to join. Write and solve an equation to find the month when both gyms have cost the same total.

Month

18. Find the mistake. Riley solved 2(x + 4) = 18 like this: 2x + 4 = 18, so 2x = 14 and x = 7. What did Riley do wrong? Find the correct answer.

Correct x =

Answer Key: Solving Equations

For the teacher

Subtract 3 from both sides → x = 5
Add 4 to both sides → x = 13
Divide both sides by 4 → x = 7
Multiply both sides by 5 → x = 30
2x = 6 → x = 3
3x = 21 → x = 7
5x = 25 → x = 5
x / 2 = 7 → x = 14
Subtract x: 2x + 2 = 8, 2x = 6 → x = 3
Subtract 2x: 3x − 4 = 11, 3x = 15 → x = 5
Subtract 4x: 3x + 3 = 18, 3x = 15 → x = 5
Subtract 2x: 4x = 20 → x = 5
2x + 2 = 4, 2x = 2 → x = 1 (or divide by 2 first: x + 1 = 2)
3x − 6 = 15, 3x = 21 → x = 7 (or x − 2 = 5)
4x + 12 = 2x + 20, 2x = 8 → x = 4
5x + 5 = 3x + 9, 2x = 4 → x = 2
30 + 10m = 15m, 30 = 5m → month 6 (both have cost $90)
Riley only multiplied the x by 2, not the 4. Correct: 2x + 8 = 18, 2x = 10 → x = 5. Check: 2(5 + 4) = 18 ✓

In the game, the scale tips when a step is done to only one side, and the Expand button multiplies every term in a group, which makes #18's mistake easy to see.