Simplifying Algebraic Expressions

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Simplifying Algebraic Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course 3
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Warm Up Simplify.
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1. 9 13 ? 5 3
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2. 16 ? 8 4 ? 1
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3. 6 9 ? 10 3
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4. 17 8 ? 20 ? 2
Course 3
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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
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Learn to combine like terms in an expression.
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Vocabulary
term like term equivalent expression simplify
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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.
Equivalent expressions have the same value for
all values of the variables.
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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 3 1 5 and 8 1 7
5y 7
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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
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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
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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
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Additional Example 2C Combining Like Terms in
Two-Variable Expressions
Combine like terms.
4m 9n 2
4m 9n 2
No like terms.
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Check It Out Example 2
Combine like terms.
A. 2x 5x 4y 3
2x 5x 4y 3
Identify like terms.
Combine coefficients 2 5 7
7x 4y 3
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.
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To simplify an expression, perform all possible
operations, including combining like terms.
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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.
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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.
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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 1 3 4
4x 48
Divide both sides by 4.
4
4
x 12
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Check It Out Example 4
Solve 7c c 102.
7c c 102
Identify like terms. The coefficient of c is 1.
Combine coefficients 7 1 6
6c 102
6c 102
Divide both sides by 6.
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c 17
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Lesson Quiz
Combine like terms. 1. 3x 4 2x 2. 13k 6
? 8m 9 k Simplify. 3. 4(3x 6) ? 7x 4.
6(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
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