Solve the inequality. Write the solution in interval notation. |5 - 8x| <= 13 Select the correct choice below, and fill in the answer box if necessary.

Question

OA. The solution set is __
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

B. There is no solution.

Answer 1

To solve the inequality |5 - 8x| <= 13, we can break it down into two cases:

Case 1: 5 - 8x >= 0
In this case, the absolute value can be removed without changing the inequality.
5 - 8x <= 13
-8x <= 8
x >= -1

Case 2: 5 - 8x < 0
In this case, we need to reverse the inequality when removing the absolute value.
-(5 - 8x) <= 13
-5 + 8x <= 13
8x <= 18
x <= 9/4

Combining the two cases, we can write the solution set in interval notation:
(-∞, -1] U (-∞, 9/4]