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.
В.
The solution set is
(Type your answer in interval notation. Simplify your answer.)
The solution set is the empty set
The given absolute value inequality is:
|8x| = 2
To solve the inequality, we can split it into two separate cases:
Case 1: 8x = 2
Solving for x in this case gives:
8x = 2
x = 2/8
x = 1/4
Case 2: 8x = -2
Solving for x in this case gives:
8x = -2
x = -2/8
x = -1/4
So the two possible solutions for x are x = 1/4 and x = -1/4. Therefore, the solution set is {1/4, -1/4}.
In interval notation, this can be written as:
(1/4, -1/4)