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.
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.
To solve the inequality |5 - 8x| <= 13, we can break it into two cases:
Case 1: 5 - 8x >= 0
In this case, the absolute value |5 - 8x| is equal to 5 - 8x. Therefore, the inequality becomes:
5 - 8x <= 13
Solving for x:
-8x <= 8
x >= -1
Case 2: 5 - 8x < 0
In this case, the absolute value |5 - 8x| is equal to -(5 - 8x), which is -5 + 8x. Therefore, the inequality becomes:
-5 + 8x <= 13
Solving for x:
8x <= 18
x <= 18/8
x <= 9/4
Combining the results from both cases, we have:
x >= -1 or x <= 9/4
Writing the solution in interval notation:
(-∞, -1] U (-∞, 9/4]
To solve the inequality |5 - 8x| <= 13, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 5 - 8x >= 0
Solving this inequality, we get:
5 >= 8x
x <= 5/8
Case 2: 5 - 8x < 0
Solving this inequality, we get:
5 < 8x
x > 5/8
Now, we need to find the intersection of the solutions from both cases. We can see that the inequality is satisfied when x is less than or equal to 5/8 and when x is greater than 5/8.
In interval notation, the solution set is (-∞, 5/8] ∪ (5/8, ∞)
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]