Question

contessa is solving an absolute value inequality. she writes the compound inequality -7 ≤ 8 - 3q ≤ 7 as her first step. which inequality is contessa solving? |8 - 3q| ≥ 7 |8 - 3q| ≥ 0 |8 - 3q| ≤ 7 |8 - 3q| ≤ 0

Explanation:

Step1: Recall absolute - value inequality rule

The absolute - value inequality \(|x|\leq a\) (where \(a\geq0\)) is equivalent to the compound inequality \(-a\leq x\leq a\).
In the given compound inequality \(-7\leq8 - 3q\leq7\), we can see that \(x = 8-3q\) and \(a = 7\).

Step2: Identify the original absolute - value inequality

Based on the rule \(|x|\leq a\Leftrightarrow - a\leq x\leq a\), the original absolute - value inequality must be \(|8 - 3q|\leq7\).

Answer:

|8 - 3q|\leq7