This document provides 18 math word problems involving distributing terms and combining like terms. Students are asked to simplify expressions by distributing terms within parentheses and combining like terms, then evaluate the expressions for given variable values. The problems cover a variety of expressions including those with addition, subtraction, multiplication, and multiple sets of parentheses.

1. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 8
Distributive Property and Combining like Terms
Essential Question: Why do we represent numbers in different ways?
Step 1 - Distribute
(only to the numbers inside the parenthesis)
Step 2 - Combine Like Terms
(leave your answer as an expression - "in terms of x")
Simplify by distributing and combining like terms. Show your work. The first one is done for you.
1. 3(x + 6) + 7x = 2. 6m + 3(m + 5) + 7 =
3 x + 18 + 7x =
10x + 18
3. 7(2 + x) + 8 = 4. 5(m + 9) + 4 =
5. 9 + 5(2x + 4) = 6. 3m + 2(5 + m) =
7. 12 + 3(x + 8) = 8. 6m + 14 + 3(m + 7) =
9. 3(7x + 2) + 8x = 10. 4(m + 6) + 3(3 + m) =

2. Step 1 - Distribute
(only to the numbers inside the parenthesis)
Step 2 - Combine Like Terms
Step 3 – Plug in given the value of the variable and solve
Simplify the expression first. Then evaluate the resulting expression for the given value of the variable.
11. 3x + 5(2x + 6) = _____ if x = 4 12. 9(2m + 1) + 2(5m + 3) = _____ if m = 2
3x + 10x + 30 =
13x + 30 =
13(4) + 30 = 82
13. 4 + 6(2x + 7) = _____ if x = 3 14. 7(7 + 5m) + 4(m + 6) = _____ if m = 1
15. 8 + 5(9 + 4x) = _____ if x = 2 16. 2(4m + 5) + 8(3m + 1) = _____ if m = 3
17. 6(4x + 7) + x = _____ if x = 2 18. 5(8 + m) + 2(7m – 7) = ______ if m = 3

3. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 8
Distributive Property and Combining like Terms
Essential Question: Why do we represent numbers in different ways?
Step 1 - Distribute
(only to the numbers inside the parenthesis)
Step 2 - Combine Like Terms
(leave your answer as an expression - "in terms of x")
Simplify by distributing and combining like terms. Show your work. The first one is done for you.
1. 3(x + 6) + 7x = 2. 6m + 3(m + 5) + 7 =
3 x + 18 + 7x = 6m + 3m + 15 + 7 =
10x + 18 9m + 22
3. 7(2 + x) + 8 = 4. 5(m + 9) + 4 =
14 + 7x + 8 = 5m + 45 + 4 =
22 + 7x 5m + 49
5. 9 + 5(2x + 4) = 6. 3m + 2(5 + m) =
9 + 10x + 20 = 3m + 10 + 2m =
29 + 10x 5m + 10
7. 12 + 3(x + 8) = 8. 6m + 14 + 3(m + 7) =
12 + 3x + 24 = 6m + 14 + 3m + 21=
36 + 3x + 24 = 9m + 35=
9. 3(7x + 2) + 8x = 10. 4(m + 6) + 3(3 + m) =
21x + 6 + 8x = 4m + 24 + 9 + 3m =
29x + 6 = 7m + 33 =

4. Step 1 - Distribute
(only to the numbers inside the parenthesis)
Step 2 - Combine Like Terms
Step 3 – Plug in given the value of the variable and solve
Simplify the expression first. Then evaluate the resulting expression for the given value of the variable.
11. 3x + 5(2x + 6) = _____ if x = 4 12. 9(2m + 1) + 2(5m + 3) = _____ if m = 2
3x + 10x + 30 = 18m + 9 + 10m + 6 =
13x + 30 = 28m + 15=
13(4) + 30 = 82 18(2) + 15=
36+15 =
51
13. 4 + 6(2x + 7) = _____ if x = 3 14. 7(7 + 5m) + 4(m + 6) = _____ if m = 1
4 + 12x + 42 49 + 35m + 4m + 24
46 + 12x 73 + 39m
46 + 12(3) 73 + 39(1)
46 + 36 73 + 39(1)
82 112
15. 8 + 5(9 + 4x) = _____ if x = 2 16. 2(4m + 5) + 8(3m + 1) = _____ if m = 3
8 + 45 + 20x = 8m + 10 + 24m + 8
53 + 20x = 32m + 18
53 + 20(2)= 32(3) + 18
53 + 40 96 + 18
93 114
17. 6(4x + 7) + x = _____ if x = 2 18. 5(8 + m) + 2(7m – 7) = ______ if m = 3
6(4x + 7) + x = 5(8 + m) + 2(7m – 7) =
24x + 42 + x = 40 + 5m + 14m – 14 =
24(2) + 42 + 2 = 40 + 5(3) + 14(3) – 14 =
48 + 42 + 2 40 + 15 + 42 – 14
90 + 2 55 + 42 – 14
92 97 – 14
83