(7) Lesson 5.6 - Simplify Algebraic Expressions

1. Identify the terms, like terms, coefficients, and constants in each
expression.
1. 8y – 3 + y 2. –22m – 2n + 1
Write each expression in simplest form.
3. 7k + 9k 4. 14h – 3 – 11h
5. Sara has x number of apples, 3 times as many oranges as apples,
and 2 peaches. Write an expression in simplest form that
represents the total number of pieces of fruit.
6. Write an expression to represent
the perimeter of the triangle.
Course 2, Lesson 5-6

2. Answers
1. terms: 8y, –3, y; like terms: 8y, y; coefficients: 8, 1;
constants: –3
2. terms: -22m, -2n, 1; no like terms; coefficients: -22, -2;
constants: 1
3. 16k
4. 3h – 3
5. 4x + 2
6. 5x + 1
Course 2, Lesson 5-6

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-6

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 5-6 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.
Course 2, Lesson 5-6 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

6. • To add linear expressions
Course 2, Lesson 5-6
Expressions and Equations

7. Course 2, Lesson 5-6
Expressions and Equations
• linear expression

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. (2x + 3) + (x + 4)
Model each linear expression.
2x + 3
So, (2x + 3) + (x + 4) = 3x + 7.
x + 4
2x x 3 4+++
Combine like tiles and write a linear
expression for the combined tiles.

9. Answer
Need Another Example?
Find (6x + 2) + (x − 3).
7x – 1

10. 1
Need Another Example?
2
Step-by-Step Example
2. (2x – 1) + (x – 5)
Arrange like terms in columns.2x – 1
+ x – 5
So, (2x – 1) + (x – 5) = 3x – 6.
3x – 6 Add.

11. Answer
Need Another Example?
Find (4x – 2) + (x – 4).
5x – 6

12. 1
Need Another Example?
2
Step-by-Step Example
3. Find (2x – 3) + (–x + 4). Use models if needed.
Model each linear expression.
2x
So, (2x – 3) + (–x + 4) = x + 1.
x
Combine like tiles. Then remove all
zero pairs and write a linear
expression for the remaining tiles.
(–3) –x 4++
+ 1

13. Answer
Need Another Example?
Find (3x – 6) + (–2x + 7). Use models if needed.
x + 1

14. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Find 2(x + 3) + (3x + 1).
Use the Distributive Property.2(x + 3) + (3x +1)
So, 2(x + 3) + (3x + 1) = 5x + 7.
Arrange like terms
in columns.
= (2 • x + 2 • 3) + (3x + 1)
= (2x + 6) + (3x + 1) Simplify
2x + 6
+ 3x + 1
5x + 7 Add.

15. Answer
Need Another Example?
Find 4(x + 1) + (5x + 2).
9x + 6

16. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. Find 5(x – 4) + (2x – 7).
Use the Distributive Property.5(x – 4) + (2x – 7)
So, 5(x – 4) + (2x – 7) = 7x – 27.
Arrange like terms
in columns.
= (5 • x – 5 • 4) + (2x – 7)
= (5x – 20) + (2x – 7) Simplify
5x – 20
+ 2x – 7
7x – 27 Add.

17. Answer
Need Another Example?
Find 3(x – 8) + (4x – 5).
7x – 29

18. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
6. Write a linear expression in simplest
form to represent the perimeter of the
triangle. Find the perimeter if the
value of x is 5 centimeters.
Write a linear expression for the perimeter of the triangle.
So, the perimeter of the triangle is 56 centimeters.
Replace x with 5. Simplify.
(3x – 3) + (2x + 9) + (5x) Write each expression.
Add.
(3x + 2x + 5x) + (–3 + 9) Rearrange to combine like terms.
10x + 6
Find the perimeter.
10x + 6 = 10(5) + 6 or 56

19. Answer
Need Another Example?
The side length of a square is (5x + 1) inches.
Write a linear expression in simplest form to
represent the perimeter of the square. Then
find the perimeter if x equals 4 inches.
20x + 4; 84 in.

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 5-6
Expressions and Equations

21. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-6
Expressions and Equations
Sample answers:
• By using algebra tiles to add linear expressions
• By combining like terms to add linear expressions
• By writing algebraic expressions in simplest form to
solve real-world problems

22. Write an explanation of
how to add two
linear expressions.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2, Lesson 5-6