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.
Like terms can be grouped together because they have the same variable raised to the same power.
Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.
Helpful Hint
Equivalent expressions have the same value for all values of the variables.

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
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Simplifying Algebraic Expressions
Check It Out: Example 1
Combine like terms.
Identify like terms; the coefficient of q is 1, because 1q = q.
A. 4q – q 3q
Combine coefficients: 4 – 1 = 3
Identify like terms; the coefficient of c is 1, because 1c = c.
B. 5c + 8 – 4c – 2 – c
Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6

9. Simplifying Algebraic Expressions
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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

10. 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

11. Simplifying Algebraic Expressions
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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.

12. Simplifying Algebraic Expressions
11-1
Simplifying Algebraic Expressions
Check It Out: Example 2
Combine like terms.
A. 2x + 5x – 4y + 3
2x + 5x – 4y + 3
Identify like terms.
7x – 4y + 3
Combine coefficients: = 7
B. 9d + 7c – 4d – 2c
9d + 7c – 4d – 2c
Identify like terms.
5d + 5c
Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5
C. 8g + c – 6
8g + c – 6
No like terms.

13. Simplifying Algebraic Expressions
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Simplifying Algebraic Expressions
To simplify an expression, perform all possible operations, including combining like terms.
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).
Remember!

14. Additional Example 3: Using the Distributive Property to Simplify
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Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive Property to Simplify
Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine coefficients 6 – 2 = 4.

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

16. Simplifying Algebraic Expressions
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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
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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
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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