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

1 Answer
MeneerNask · Meave60
Aug 10, 2015

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}

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