Question

find the solution for the equation
|2x-8|+2=7

Answer 1

how do you find the solution set

Answer 2

\[|2x-8|+2=7 \implies |2x-8|=5.\]
This is true for two cases:
Case 1: \(2x-8=5 \implies 2x=13 \implies x=\frac{13}{2}\).
Case 2: \(2x-8=-5 \implies 2x=3 \implies x=\frac{3}{2}\).

Answer 3

If you're stuck, you could remember the definition\[|a|=b\implies-b=a=b.\]

Answer 4

|2x -8|+2=7
so, either (2x-8)+2 = 7 or -(2x-8)+2 = 7
2x-6=7 -2x+10=7
2x=13 2x=3
x=13/2 x=3/2