Question

Which of the following are solutions to | x-1|= 5x + 2 ? Check all that apply.

Answer 1

x = -1/6

Explanation:

this was the only right one

Answer 2

By definition of absolute value, if
`x-1\ge0`, then
`|x-1|=x-1`, so

`|x-1|=5x+2\implies x-1=5x+2\implies4x=-3\implies x=-\frac34`

On the other hand, if
`x-1<0`, then
`|x-1|=-(x-1)=1-x`, and

`|x-1|=5x+2\implies1-x=5x+2\implies6x=-1\implies x=-\frac16`