Question

a nursery sells young palm trees. they guarantee that a palm tree will grow to be 7 feet tall, plus or minus 1.5 feet. if the tree’s height doesn’t meet this guarantee after 2 years, a refund can be issued. (a) let x represent the height (in feet) of a palm tree. write an absolute value inequality that can be used to find the acceptable heights of a palm tree. these are the heights where the guarantee is met.

Explanation:

Step1: Define target and tolerance

Target height = 7 ft, tolerance = 1.5 ft.

Step2: Set up absolute value inequality

The absolute difference between the tree's height $x$ and the target height must be within the tolerance for the guarantee to hold:
$$|x - 7| \leq 1.5$$

Answer:

$|x - 7| \leq 1.5$