Solve the following absolute value inequality
8x|=2
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
А.
The solution set is ____
(Type your answer in interval notation. Simplify your answer.)
B. The solution set is the empty set
To solve the absolute value inequality |8x| = 2, we can split it into two separate cases:
Case 1: 8x = 2
Divide both sides by 8:
x = 2/8
Simplify:
x = 1/4
Case 2: 8x = -2
Divide both sides by 8:
x = -2/8
Simplify:
x = -1/4
Therefore, the solution set is { -1/4, 1/4 }.
In interval notation, this can be written as (-1/4, 1/4).
So, the correct choice is:
А. The solution set is (-1/4, 1/4)