Solve the following absolute value equation
|4x - 22| - 5= -3
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.)
• B. The solution set is the empty set, ().
To solve the absolute value equation |4x - 22| - 5 = -3, we can start by isolating the absolute value term. Add 5 to both sides of the equation:
|4x - 22| = 2
Next, we split the equation into two separate equations, one positive and one negative:
4x - 22 = 2 or 4x - 22 = -2
Solve the positive equation:
4x - 22 = 2
Adding 22 to both sides:
4x = 24
Dividing by 4:
x = 6
Now solve the negative equation:
4x - 22 = -2
Adding 22 to both sides:
4x = 20
Dividing by 4:
x = 5
The solutions to the absolute value equation are x = 6 and x = 5.
So, the correct choice is A. The solution set is {5, 6}.