Lesson 15

Lesson 15

Equivalent Expressions

What is a term?

A term is a number, a variable, or the product of numbers, variables, and/or expressions

Multiple Choice

Which of these is NOT a term?

• 15

• z

• 5a

• 3 + 2b

What are equivalent expressions?

3x + 5y + 2z + 8y - 2x -3y is the same as 1x + 2y + 2z

By combining like terms you can make equivalent expressions

Equivalent Expressions

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Multiple Choice

Which one of these is equivalent to

3x + 12y + 7z + 14x + 13 + 12 +5y?

• 17 x + 17y +20z + 13

• 15x + 21 z + 25 + 5y

• 17x + 17y + 7z + 25

• 3x + 12y + 7z + 13

Multiple Select

Which expressions are equivalent to

2(3x + 8 + 4x)?

• 6x + 16 + 8x

• 6x + 4x + 8

• 10x + 8

• 14x + 16

Multiple Choice

True or False?

7(-5b + 4) = -35b + 28

• True

• False

Substituting a value for a variable in an expression

If x = 4 what is the value for 3x + 12?
This would be  $3\cdot4\ +\ 12$  Which would become 12 + 12 = 24

Multiple Choice

What is the value of this expression if x = 8?

4(2x + 3)

• 11

• 19

• 64

• 76

Multiple Choice

 $12x\ +\ \frac{1}{2}\ -\ 4\ x\ -\ 8.5\ +\ 2x\ +\ 8$ 

 Evaluate this expression if x = 6.

• 30

• 40

• 50

• 60

How do you factor an expression?

Find the greatest common factor of each term.

Factor this expression and simplify

 $24y\ -\ 36\ +\ 12\ -\ 12\ y\ +\ 24\ -\ 48y$  

The GCF of each term is 12 so,

 $12\left(2y\ -\ 3+\ 1\ -1y\ +\ 2\ -\ 4y\right)$  
and then simplify - 
 $12\left(-3y\right)$  

Multiple Choice

 $3y\ -9\ +\ 12y\ +\ 12\ -\ 6$  

Factor, combine like terms, and simplify the expression above. 

Which one of these answers correctly shows this expression simplified?

• 3(5y)

• 3(5y - 1)

• 5(3y - 1)

• 5 (3y)

Multiple Choice

 $-2\left(10m\ -\ 4\right)\ +\ \left(2\ +\ 4m\ -\ 1\right)$ 
Simplify the expression above.

Which one of these is equivalent to this expression?

• -14 m + 10

• -16m + 9

• -24m - 9

• 16m + 10

Summary of lesson 15

• What is a term?

• Combining Like terms

• Using the distributive property

• Simplifying expressions

• Evaluating Expressions

• Factoring to simplify an expression