Solve the following absolute value equation.

Question

4|5 - 12x| = 24
Select the correct choice below and, if necessary, fill in the answer box to complete your choice
• A. The solution set is ___
(Simplify your answer. Use a comma to separate answers as needed.)
• в.
The solution set is the empty set, { }

Answer 1

To solve the absolute value equation 4|5 - 12x| = 24, we can start by isolating the absolute value term.

Divide both sides of the equation by 4:
|5 - 12x| = 6

Now, we can split the equation into two separate cases:
1) 5 - 12x = 6
2) 5 - 12x = -6

Solve Case 1:
5 - 12x = 6
-12x = 6 - 5
-12x = 1
x = 1/(-12)
x = -1/12

Solve Case 2:
5 - 12x = -6
-12x = -6 - 5
-12x = -11
x = -11/(-12)
x = 11/12

So the solution set is {-1/12, 11/12}. Therefore, the correct choice is:
• A. The solution set is {-1/12, 11/12}