The solutions are S={2,4}
Step-by-step explanation:
Let's rewrite the equation
|3x−8|−x=0
|3x−8|=3x−8, if 3x−8≥0
and
|3x−8|=−(3x−8)=−3x+8, if 3x−8<0
Let f(x)=|3x−8|−x=0
Let's build a variation table
aaaaxaaaaaaaa−∞aaaaaaaa0aaaaaaaaaa83aaaaaaa+∞
aaaaxaaaaaaaaaaaaa−aaaa#color(white)(aaaaa)+#aaaaaaaa+
aaaa|3x−8|aaaaaa−3x+8a#color(white)(aaa)-3x+8#aaaaa3x−8
aaaaf(x)aaaaaaaaaaax=2a#color(white)(aaaaa)x=2#aaaaaax=4
The solutions are S={2,4}
graph