Question

I'm trying to solve the following inequality and list in inverval notation:
8 - |2x - 1| >= 6

Answer 1

I first tried dividing all by 8 and originally got [-1/4,1/2] but that answer was wrong.

Answer 2

8 - |2x - 1 | >= 6 --- subtract 8
-|2x - 1| >= 6 - 8
-|2x - 1| >= -2 -- divide by -1
|2x - 1| <= 2

(2x - 1) <= 2
2x <= 2 + 1
2x <= 3
x <= 3/2

(2x - 1) >= -2
2x >= -2 + 1
2x >= -1
x >= -1/2

-1/2 <= x <= 3/2

interval notation : [-1/2,3/2]