Hi !
f(x) = x + |2x − 1|
We have the function at hand,so if the function is equal to 8,then x + |2x − 1| is equal to 8 too :
x + |2x − 1| = 8
Now we can express the module so:
|2x − 1| = 8-x
It means we'll have 2 options :
I : 2x-1 = 8-x
II : 2x-2 = -(8-x)
I : 2x-1 = 8-x | +x
2x-1+x = 8-x+x
3x-1 = 8 | + 1
3x-1+1 = 8+1
3x = 9 | ÷ 3
x = 3
II : 2x-1 = -(8-x)
2x-1 = -8+x | -x
2x-x-1 = -8+x-x
x-1 = -8 | +1
x-1+1 = -8+1
x = -7
Solutions : 3,-7
