Solve the following absolute value equation.
3| - 8x - 9|- 6=15
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ____
• B. There is no solution.
(Simplify your answer. Type integers or simplified fractions. Use a comma to separate answers as needed.)
3| - 8x - 9|- 6=15
First, let's isolate the absolute value expression by adding 6 to both sides of the equation:
3| - 8x - 9| = 15 + 6
Simplifying,
3| - 8x - 9| = 21
Next, divide both sides of the equation by 3:
| - 8x - 9| = 21/3
| - 8x - 9| = 7
Now, we need to consider the two possible cases for the absolute value:
Case 1: - 8x - 9 = 7
By solving for x, we have:
- 8x - 9 = 7
- 8x = 7 + 9
- 8x = 16
x = 16/(-8)
x = -2
Case 2: -(- 8x - 9) = 7
Simplifying,
8x + 9 = 7
8x = 7 - 9
8x = -2
x = -2/8
x = -1/4
Therefore, the solution set is { -2, -1/4 }
The answer is A. The solution set is { -2, -1/4 }