1. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3

2. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Warm Up
Simplify.
 5 + 3 20
2. 16   1 11  8
 20  2 3
Course 3

3. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Problem of the Day
Ray and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see?
7 turkeys, 8 deer

4. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Learn to combine like terms in an expression.

5. Vocabulary 11-1 Simplifying Algebraic Expressions term like term
equivalent expression
simplify

6. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Terms in an expression are separated by plus or minus signs.
Variable: A letter used to represent a mystery number.
Like terms can be grouped together because they have the same variable raised to the same power.
Constant: A number without a variable. All constants can be combined because they are like terms.
Coefficient: The number in front of a variable. This number is being multiplied by the variable.

7. Additional Example 1: Combining Like Terms To Simplify
11-1
Simplifying Algebraic Expressions
Additional Example 1: Combining Like Terms To Simplify
Combine like terms.
A. 14a – 5a
Identify like terms. 9a
Combine coefficients: 14 – 5 = 9
Identify like terms ; the coefficient of y is 1, because 1y = y.
B. 7y + 8 – 3y – 1 + y
Combine coefficients: 7 – = 5 and 8 – 1 = 7
5y + 7

8. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Additional Example 2A: Combining Like Terms in Two-Variables Expressions
Combine like terms.
9x + 3y – 2x + 5
9x + 3y – 2x + 5
Identify like terms.
7x + 3y + 5
Combine coefficients: 9 – 2 = 7

9. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Additional Example 2B: Combining Like Terms in Two-Variable Expressions
Combine like terms.
5t + 7p – 3p – 2t
5t + 7p – 3p – 2t
Identify like terms.
Combine coefficients: 5 – 2 = 3 and 7 – 3= 4
3t + 4p

10. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Additional Example 2C: Combining Like Terms in Two-Variable Expressions
Combine like terms.
4m + 9n – 2
4m + 9n – 2
No like terms.

11. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
The Distributive Property:
states that a(b + c) = ab + ac for all real numbers a, b, and c.
For example: 2(3 + 5) = 2(3) + 2(5).

12. Additional Example 3: Using the Distributive Property to Simplify
11-1
Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property to Simplify
Simplify 6(5 + n) – 2n.
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine like terms.
6 – 2 = 4.

13. Additional Example 3: Using the Distributive Property to Simplify
11-1
Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property to Simplify
Simplify 5(3 + 2n) – n.
5(3) + 5(2n) – n
Distributive Property.
n – n
Multiply.
15 + 9n
Combine like terms

14. Additional Example 3: Using the Distributive Property to Simplify
11-1
Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property to Simplify
Simplify 5(6 – 5x) + 10.
5(6) - 5(5x) + 10
Distributive Property.
30 – 25x + 10
Multiply.
Combine like terms
40 – 25x

15. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Check It Out: Example 3
Simplify 3(c + 7) – c.
3(c) + 3(7) – c
Distributive Property.
3c + 21 – c
Multiply.
2c + 21
Combine like terms
3 – 1 = 2.

16. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Additional Example 4: Combining Like Terms to Solve Algebraic Equations
Solve x + 3x = 48.
x + 3x = 48
Identify like terms. The coefficient of x is 1.
4x = 48
Combine coefficients: = 4
4x = 48
Divide both sides by 4. 4 4
x = 12

17. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Check It Out: Example 4
Solve 7c – c = 102.
7c – c = 102
Identify like terms. The coefficient of c is 1.
6c = 102
Combine coefficients: 7 – 1 = 6
6c = 102
Divide both sides by 6. 6 6
c = 17

18. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Lesson Quiz
Combine like terms.
1. 3x x k + 6  8m k
Simplify.
3. 4(3x + 6)  7x (x + 5) + 3x
Solve.
5. 6y + y = 42
6. The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens?
5x + 4
14k – 8m + 15
5x + 24
9x + 30
y = 6 $3