Solve each of the absolute value equations algebraically.

Question

|(x/2)+3|=3x-3

Now the work isn't an issue, I did all that & I have my answer. My problem is, I double checked my answer on mathways & it said only my first answer: x=(12/5) but I also got x=0 & when double checked that checks out... Is there a reason that 0 can't be a suitable answer?

Thanks a bunch! :)

Answer 1

Well, first of all let's look at
|(x/2)+3|=3x-3 , and just follow the definition of |....|, it has to be zero or positive, so
3x-3 ≥ 0
x ≥ 1
I will trust your algebra, and that you got x = 0
but x≥ 1, so x cannot be zero

you could have also checked that answer:
if x = 0
LS = |0/2+3| = 3
RS = 3(0) - 3 = -3
so it did not work!!

Answer 2

Thank you so much, that makes total sense, I wasn't thinking about that & now I am!