Question

What is the solution set for `abs(2x – 6) – 7 = 7`?

Answer 1

With absolutes you usually end up solving two equations.

Explanation:

But first we simplify, as long as we don't interfere with the sign inside the brackets:

Add 7, then divide by 2:
`->|2x-6|=14->|x-3|=7`

Now we have two possibilities:
(1)
`x>=3->x-3>=0` the brackets don't have to do their work:
Add 3:
`x-3=7->x=10`
(2)
`x<3->x-3<0` the brackets flip the sign:
`-(x-3)=7->-x+3=7->x=-4`

Answer : `{x=-4orx=+10}`