Question

give the solution set in both interval and graph form. |8 - x| ≤ 7 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is 1,15. (type your answer in interval notation.) b. the solution set is ∅. choose the correct graph below.

Explanation:

Step1: Solve the absolute - value inequality

Given \(|8 - x|\leq7\). By the property of absolute - value inequalities \(|a|\leq b\) (\(b\geq0\)) which is equivalent to \(-b\leq a\leq b\). Here \(a = 8 - x\) and \(b = 7\), so \(-7\leq8 - x\leq7\).
Subtract 8 from all parts of the compound inequality:
\(-7-8\leq8 - x-8\leq7 - 8\)
\(-15\leq - x\leq - 1\).
Multiply all parts by \(-1\) (and reverse the inequality signs):
\(1\leq x\leq15\).

Step2: Determine the interval notation

The interval notation for \(1\leq x\leq15\) is \([1,15]\).

Step3: Analyze the graph

For the inequality \(1\leq x\leq15\), on the number - line, we have a closed circle at \(x = 1\) (because \(x = 1\) is included in the solution set, since the inequality is \(\leq\)) and a closed circle at \(x = 15\) (because \(x = 15\) is included in the solution set), and the line segment between them.

Answer:

A. The solution set is \([1,15]\)
C. (The graph with a closed circle at \(1\), a closed circle at \(15\), and the line segment between them)