contessa is solving an absolute value inequality. she writes the compound inequality -7 ≤ 8 - 3q ≤ 7 as her…

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

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

Answer

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