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

1 Answer
Aug 10, 2015

Answer:

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}#