How do you solve #|6- 2x | = 2| x - 3|#?

1 Answer
Nov 25, 2016

This equation is an identity, so true for any value of #x#

Explanation:

Any positive scalar factor can be moved outside the #|...|# and for any number #a#, #abs(a) = abs(-a)#.

So we find:

#abs(6-2x) = abs(2(3-x)) = 2abs(3-x) = 2abs(x-3)#

for any value of #x#.

The solution space is the whole of #RR#.