Question

To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?

10(1/2x+2)-5=3(x-6)+1

A) –32 and 2

B) –2 and 32

C) –2 and 2

D) –32 and 32

Answer 1

I think it is c but it could also be d

Answer 2

Option C is correct .i.e., 2 and -2

Explanation:

Given Expression:
`10((1)/(2)x+2)-5=3(x+6)+1`

Step 1: the distributive property

`10*(1)/(2)x+10*2-5=3*x+3*6+1`

`5x+20-5=3x+18+1`

Step 2: combines like terms

`5x+15=3x+19`

Step 3: then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side

`5x-3x=19-15`

`2x=4`

Therefore, Option C is correct