Question

Let f(x)=|2x+10| and g(x)=|2x-24| . Find all values of x for which f(x)=g(x) .

Answer 1

f(x)=g(x)
|2x+10|=|2x-24|
Case 1:
2x+10=2x-24
0=-34
No Solutions
Case 2:
2x+10=-2x+24
4x=14
x=7/2
The other two cases are equivalent so the only solution is x=7/2

think about why the other two cases are equivalent.

Answer 2

because one this time the opposite side is negative and when both sides become negative its like them being positive