5. (912.ar.4.1 building to proficiency) the recommended storage temperature for a certain type of cheese is…

Explanation:

Step1: Set up the absolute - value equation

Let $t$ be the storage temperature. The distance between $t$ and 45 is within 8. We can write the absolute - value equation as $|t - 45|\leq8$.

Step2: Rewrite the absolute - value inequality as a compound inequality

The absolute - value inequality $|x|\leq a$ ($a\geq0$) is equivalent to $-a\leq x\leq a$. So, $|t - 45|\leq8$ is equivalent to $- 8\leq t - 45\leq8$.

Step3: Solve the compound inequality

Add 45 to all parts of the compound inequality: For the left - hand side: $-8+45\leq t-45 + 45$, which simplifies to $37\leq t$. For the right - hand side: $t-45 + 45\leq8 + 45$, which simplifies to $t\leq53$.

Answer:

The recommended storage temperature range is $37^{\circ}F\leq t\leq53^{\circ}F$.