SOLUTION: please show how to Solve the absolute value inequality, please Write interval notation for the solution set |10x – 8| ≤ 32

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Question 1055766: please show how to Solve the absolute value inequality, please Write interval notation for the solution set
|10x – 8| ≤ 32
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
factorize the positive number, 2, from the absolute value:
2%2Aabs%285x-4%29%3C=32
and then
abs%285x-4%29%3C=16

Solve for the two possible conditions of 5x-4; that it be less than zero, or that it be non-negative.

If nonnegative,
5x-4%3C=16
5x%3C=20
x%3C=4
If negative,
-5x%2B4%3C=16
-5x%3C=12
x%3E=-12%2F5
or
x%3E=-2%262%2F5

Putting these two solution parts together,
highlight%28-2%262%2F5%3C=x%3C=4%29