Question

Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their answers to get the same expression. What are the values missing from Gregory's expression?

Answer 1

see the explanation

Explanation:

we have

Felicia

`-5(3x+2)+10x`

Apply distributive property

`-5(3x)-5(2)+10x`

`-15x-10+10x`

Combine like terms

`-5x-10`

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant term in Gregory's expression

so

`-12-4x+ax+b`

equate Gregory's expression to Felicia's expression

`-12-4x+ax+b=-5x-10`

so

`-12+b=-10` ----->
`b=2`

`-4x+ax=-5x` ------>
`a=-1`

so

Gregory's expression is

`-12-4x+2-x`

therefore

The missing terms are 2 and -x