Equivalent 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

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.

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).

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