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Warm-Up Using Properties to Simplify Expressions

Lesson Goals

Define equivalent expressions.

Identify expressions thatare equivalent by using

of operations.

Evaluate expressions to determine

if they are .

Words to Know

Fill in this table as you work through the lesson. You may also use the glossary to help you.

equivalent having the amount, value, area, volume, or force

evaluate to determine the of

commutative property

the property stating that changing the in which two

numbers are added or multiplied does not change the value of the sum or product

like termsterms consisting of the same , raised to the

same

Lesson Question

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WK2

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Using Properties to Simplify ExpressionsInstruction

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Equivalent Expressions

Two expressions are equivalent if they are for all possible values of the variables.

What is an equivalent expression for −2.5 + 7.1x?

1. Use properties of

to rewrite the expression.

• Use the commutative property.

−2.5 + 7.1x

7.1x + (   )7.1x − 2.5

Visually Representing Equivalent Expressions

+ + + + +− x

− x

− x

1. Model the expression withalgebra tiles.

2. Combine the x terms.

(  ) + 3 + 23. Combine the constant terms.

(−3x) +

We can use an interactive to group like terms and write an equivalent expression.

(−2x) + 3 + (−x) + 2

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Using Properties to Simplify ExpressionsInstruction

Equivalent Expressions

STRATEGY

What is an equivalent expression for 34

5

711

2

7− + +x x ?

1. Use properties of operations to rewrite the expression.

• Use the

property.

2. Combine .

• Rewrite the coefficient 11 with a denominator of 4.

3

411

5

7

2

7+ − +x x

3

4

44

4

5

7

2

7+ − +x x

47

4−x

This expression is to the original expression.

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Using Properties to Simplify ExpressionsInstruction

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Determining whether Expressions Are Equivalent

STRATEGY

Is −0.58x + 2.27 equivalent to 7.037 1.798

3.1

− x ?

Use to evaluate the expressions.

Let x = 0.

= 2.27

The expressions are equivalent for 0.

In order to be equivalent, the expressions must be equal when value of x is used. 

Let x = 10.

First expression:

−0.58(10) + 2.27

−5.8 + 2.27

−3.53

Second expression:

−7.037 1.798(10)

3.1

7.037 17.98

3.1

−

−10.9433.1

We can conclude that these two expressions are .

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Using Properties to Simplify ExpressionsInstruction

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Examples and Nonexamples

You should evaluate with numbers other than 0, because sometimes using x = 0

will give a equivalency.

Equivalent Expressions Expressions

−0.58x + 2.27 and 7.037 1.798

3.1

− x −0.58x + 2.27 and 7.037 2.798

3.1

− x

If we evaluate the expressions, for x = 0, the values are equivalent.

If we substitute x = 1 we get 1.69 on the left and approximately 1.37 on the right.

Expressions with Multiple Variables

Is 23

3

4

1

6

1

2− − +x y x y equivalent to 1

2

1

2

1

4− +x y y ?

Substitute values for both x and y.

x = 6 y = 4

2

36

3

44

1

66

1

24( ) ( ) ( ) ( )− − +

4 − − 1 + 22

1

26

1

24

1

44( ) ( ) ( )− +

3 − 2 +

The expressions are .

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Using Properties to Simplify ExpressionsInstruction

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Equivalent Expressions for Tax

A store charges 6% sales tax. The total cost of an item with price p is p + 0.06p. What is an equivalent expression?

p = 10

p + 0.06p

10 + 0.06 (10)

10 + 10.6

1.06p

1.06(  )

So, the expressions are .

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Summary Using Properties to Simplify Expressions

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Answer

Review: Key Concepts

Equivalent expressions:

• are equal for value of the variable.

• can be reduced or rewritten to look the .

Only real value for the variable that shows expressions that are not

equal is enough to prove the expressions are not equivalent.

Lesson Question How can you tell if two expressions are equivalent?

2

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Summary Using Properties to Simplify Expressions

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