Question

Which equation has solution x = -3?

A) 2x - 7 = -1

B) 3x + 8 = 1

C) 1
2
x + 8 = 10

D) 1
2
(2x - 6) = -6

Answer 1

D

Explanation:

If we solve A, it comes to 2x=6 (adding 7 to both sides.) and x comes to x=positive 3

If we solve B, it comes to: 3x=-7 (subtracting 8 from both sides) and x would equal -7/3.

If we solve C, it comes to 1/2x=2 (subtracting 8 from both sides) and x would equal 4.

If we solve D, first we have to distribute so the equation becomes x-3=-6 which comes to x=-3 (adding 3 to both sides.)

Answer 2

`\boxed {\sf D}`

Explanation:

`\sf A.\: 2x - 7 = -1`

`\sf 2x-7+7=-1+7`

`\sf 2x=6`

`\sf \cfrac{2x}{2}=\cfrac{6}{2}`

`\boxed {\sf x=3}`

`\boxed{\sf NO}`

___________________

`\sf B.\:3x + 8 = 1`

`\sf 3x+8-8=1-8`

`\sf 3x=-7`

`\sf \cfrac{3x}{3}=\cfrac{-7}{3}`

`\boxed {\sf x=-(7)/(3)}`

`\boxed{\sf NO}`

_____________________

`\sf \cfrac{1}{2}\:x+8=10`

`\sf \cfrac{1}{2}\:x+8-8=10-8`

`\sf \cfrac{1}{2}\:x=2`

`\sf 2* \cfrac{1}{2}\:x=2* \:2`

`\boxed{\sf x=4}`

`\boxed {\sf NO}`

_____________________

`\sf D.\: \cfrac{1}{2}\left(2x-6\right)=-6`

`\sf 2* \cfrac{1}{2}\left(2x-6\right)=2\left(-6\right)`

`\sf x-6=-12`

`\sf 2x-6+6=-12+6`

`\sf 2x=-6`

`\sf \cfrac{2x}{2}=\cfrac{-6}{2}`

`\boxed{\sf x=-3}`

`\boxed{\sf YES\: \checkmark }`

______________________