To subtract two linear expressions: 1. Arrange the like terms in column form with the subtrahend expression underneath the minuend. 2. Take the additive inverse of the subtrahend expression by changing the sign of each term. 3. Add the subtrahend expression with its inverse to the minuend expression. 4. Simplify the resulting expression.

1. Course 2, Lesson 5-7
Add. Use models if needed.
1. (3x + 6) + (3x – 5 )
2. (–2x + 3) + (3x + 3)
3. (x + 4) + (–2x – 6)
4. (5x + 4) + (7x + 1)
5. At the gym, Tika spends twice as much time doing aerobics than
weight training. She stretches for one fifth of the time she
spends on weight training. Let w be the amount of time Tika
spends on weight training. Write an expression to represent her
total workout.

2. ANSWERS
1. 6x + 1
2. x + 6
3. –x – 2
4. 12x + 5
5. 2w + w + ;
Course 2, Lesson 5-7
5
w 1
3
5
w

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-7

4. • 7.EE.1
Apply properties of operations as strategies to add, subtract, factor,
and expand linear expressions with rational coefficients.
• 7.EE.2
Understand that rewriting an expression in different forms in a
problem context can shed light on the problem and how the quantities
in it are related.
Course 2, Lesson 5-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Expressions and Equations
Course 2, Lesson 5-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.

6. • To subtract linear expressions with
algebra tiles
• To subtract linear expressions by
adding the opposite, or additive
inverse
Course 2, Lesson 5-7
Expressions and Equations

7. 1
Need Another Example?
2
3
Step-by-Step Example
1. Subtract (6x + 3) – (2x + 2). Use models if needed.
There are four x-tiles and one 1-tile remaining.
To subtract 2x + 2, remove two x-tiles
and two 1-tiles. Then write the linear
expression for the remaining tiles.
So, (6x + 3) – (2x + 2) = 4x + 1.
Model the linear expression 6x + 3.
6x 3+
4x 1+

8. Answer
Need Another Example?
Find (4x + 1) – (3x + 5). Use models if needed.
x – 4

9. 1
Need Another Example?
2
3
Step-by-Step Example
2. Subtract (2x – 3) – (x – 2). Use models if needed.
There is one x-tile and one –1-tile remaining.
To subtract x – 2, remove one x-tile and
two –1-tiles. Then write the linear
expression for the remaining tiles.
So, (2x – 3) – (x – 2) = x – 1.
Model the linear expression 2x – 3.
2x (–3)+
x (–1)+

10. Answer
Need Another Example?
Find (4x – 6) – (2x – 4). Use models if needed.
2x – 2

11. 1
Need Another Example?
2
3
Step-by-Step Example
3. Find (–2x – 4) – (2x). Use models if needed.
Since there are no positive x-tiles
to remove, add two zero pairs of x-
tiles. Remove two positive x-tiles.
So, (–2x – 4) – (2x) = –4x – 4.
Model the linear expression –2x – 4.
2x (–4)+
zero pairs

12. Answer
Need Another Example?
Find (–7x – 6) – (7x). Use models if needed.
–14x – 6

13. 1
Need Another Example?
2
Step-by-Step Example
4. Find (6x + 5) – (3x + 1).
Arrange like terms in columns.6x + 5
(+) –3x – 1
3x + 4
The additive inverse of 3x + 1 is (–3x – 1).

14. Answer
Need Another Example?
Find (12x + 8) – (6x + 2).
6x + 6

15. 1
Need Another Example?
2
Step-by-Step Example
5. Find (–4x – 7) – (–5x – 2).
Arrange like terms in columns.–4x – 7
(+) 5x + 2
x – 5
The additive inverse of (–5x – 2) is (5x + 2).

16. Answer
Need Another Example?
Find (–5x – 9) – (–6x – 1).
x – 8

17. 1
Need Another Example?
2
3
4
Step-by-Step Example
6. A hat store tracks the sale of college and professional team hats for m months.
The number of college hats sold is represented by (6m + 3). The number of
professional hats sold is represented by (5m – 2). Write an expression to show
how many more college hats were sold than professional hats. Then evaluate
the expression if m equals 10.
Arrange like terms in columns.
Find (6m + 3) – (5m – 2).
The additive inverse of 5m – 2 is (–5m + 2).
6m + 3
(+) –5m + 2
m + 5
Substitute 10 for m.
Evaluate the expression if m = 10.
Simplify.
m + 5 = 10 + 5
= 15
So, 15 more college team hats were sold.

18. Answer
Need Another Example?
A bakery wants to know how many more chocolate chip
cookies than sugar cookies were sold last month. The
number of chocolate chip cookies sold is represented
by the expression 7n + 6. The number of sugar cookies
sold is represented by the expression 6n – 3. Write an
expression to show how many more chocolate chip
cookies were sold last month. Then evaluate the
expression if n equals 15.
n + 9; 24

19. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-7
Expressions and Equations

20. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-7
Expressions and Equations
Sample answers:
• By adding the opposite, or additive inverse, to subtract
linear expressions
• By subtracting linear expressions to solve real-world
problems

21. Write an explanation of how
to subtract two
linear expressions.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2, Lesson 5-7