Solve the inequality. Write the solution in interval notation.
StartAbsoluteValue 8 minus 7 x EndAbsoluteValue less than or equals 15
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Part 1
Select the correct choice below, and fill in the answer box if necessary.
A.
The solution set is enter your response here
.
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)
The solution set is (-∞, ∞).
no
I apologize for the mistake. Let's solve the inequality step by step:
|8 - 7x| ≤ 15
We can break this inequality into two separate inequalities:
8 - 7x ≤ 15 and 8 - 7x ≥ -15
Solving the first inequality:
8 - 7x ≤ 15
-7x ≤ 7
x ≥ -1
Solving the second inequality:
8 - 7x ≥ -15
-7x ≥ -23
x ≤ 23/7
Since |8 - 7x| can be less than or equal to 15 if x is greater than or equal to -1 or less than or equal to 23/7, the solution set is (-∞, -1] U [23/7, ∞).
To solve the inequality |8 - 7x| ≤ 15, we need to consider two cases: when the expression inside the absolute value is positive, and when it is negative.
Case 1: When 8 - 7x is positive (8 - 7x ≥ 0)
8 - 7x ≥ 0
-7x ≥ -8 (subtracting 8 from both sides)
x ≤ 8/7 (dividing by -7, and reversing the inequality)
Case 2: When 8 - 7x is negative (8 - 7x < 0)
8 - 7x < 0
-7x < -8 (subtracting 8 from both sides)
x > 8/7 (dividing by -7, and reversing the inequality)
Now, let's put the solutions from both cases together:
x ≤ 8/7 or x > 8/7
We can represent this solution set in interval notation as:
(-∞, 8/7] U (8/7, ∞)
So, the solution set is (-∞, 8/7] U (8/7, ∞).