Equivalent Expressions

Equivalent Expressions

10/9/20

Your Mission

Your goal with this lesson is to figure out which of the following expressions are equivalent and why?

a) 2(x+4)

b) 8+2x

c) 2x+4

d) 3(x+4)−(4+x)

e) x+4

Properties to Solve Expressions

• we have to transform expressions using special properties of math. We use the properties to decide if two different expressions are equivalent.

• There 3 main Math properties used to solve expressions:

• Commutative

• Distributive

• Associative

Distributive Property

• The first step to solving this problem is using the distributive property to get rid of the parentheses for choices a and d

• To rewrite (a), we can use the distributive property: 2(x+4)=2x+8

• With the distributive property, the 2 gets multiplied with x to make 2x.

• Then the 2 also gets multiplied with the 4 to make 8.

Commutative Property

• Let's learn about another property that will help us solve this problem - The Commutative Property

• The Commutative Property tells us that the order of two numbers that are added or multiplied does not change their sum or product (ex: 2 + 3 = 3 +2 or 4 × 7 = 7 × 4).

Now put that knowledge to use...

• Let's try and solve expression d)3(x+4)−(4+x)

• 3(x+4)−(4+x) =3(x+4)−(x+4) [commutative property of addition]

• 3x+12-4-1x [use distributive property]

• 3x-1x+12-4 [combine like terms]

• =2x+8