To determine which absolute value inequality Contessa is solving, we start with the compound inequality she wrote:
[tex]\[ -7 \leq 8 - 3q \leq 7 \][/tex]
### Step-by-Step Process
1. Recognize the Form of an Absolute Value Inequality:
An absolute value inequality [tex]\(|A| \leq B\)[/tex] can be rewritten as:
[tex]\[ -B \leq A \leq B \][/tex]
Similarly, an absolute value inequality [tex]\(|A| \geq B\)[/tex] can be rewritten as:
[tex]\[ A \leq -B \text{ or } A \geq B \][/tex]
2. Compare the Given Inequality:
Looking at the compound inequality Contessa wrote:
[tex]\[ -7 \leq 8 - 3q \leq 7 \][/tex]
We notice that it matches the standard form of [tex]\(-B \leq A \leq B\)[/tex], where [tex]\(A = 8 - 3q\)[/tex] and [tex]\(B = 7\)[/tex].
3. Determine the Equivalent Absolute Value Inequality:
Given the structured form above, we rewrite the compound inequality as:
[tex]\[ |8 - 3q| \leq 7 \][/tex]
Therefore, the absolute value inequality that Contessa is solving is:
[tex]\(\boxed{|8 - 3q| \leq 7}\)[/tex]
This aligns with the third option provided:
[tex]\[ |8 - 3q| \leq 7 \][/tex]
