Question

(b) solve the absolute value inequality from part (a).
7.5 ≤ x ≤ 8.5
(c) graph the solution from part (b) on the number line below.
(d) fill in the blanks.
the palm tree will meet the guarantee if it grows to be select feet tall, and select feet tall.

Explanation:

Step1: Confirm inequality solution

The given solution is $7.5 \leq x \leq 8.5$.

Step2: Graph the solution

On the number line:

1. Plot closed dots at $7.5$ and $8.5$ (since the inequality includes equality, $\leq$ and $\geq$).
2. Draw a solid line segment connecting the two dots to represent all values between them.

Step3: Fill in the blanks

Match the inequality to the statement: the palm tree meets the guarantee if it is at least 7.5 feet tall, and at most 8.5 feet tall.

Answer:

(b) The solved absolute value inequality is $\boldsymbol{7.5 \leq x \leq 8.5}$
(c) Graph: Closed dots at 7.5 and 8.5, with a solid line connecting them on the number line.
(d) The palm tree will meet the guarantee if it grows to be at least 7.5 feet tall, and at most 8.5 feet tall.