Question
A nursery sells young palm trees. They guarantee that a palm tree will grow to be 3 feet tall, plus or minus 0.5 feet. If the tree’s height doesn’ guarantee after 2 years, a refund can be issued.
(a) Let
represent the height (in feet) of a palm tree. Write an absolute value inequality that can be used to find the unacceptable heights These are the heights where the guarantee is not met, and a refund can be issued.
-
-
(b) Solve the absolute value inequality from part (a).
and
or
(a) Let
(b) Solve the absolute value inequality from part (a).
Ask by Bowen Curry. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Part (a):
The unacceptable heights are represented by the absolute value inequality:
The unacceptable heights are represented by the absolute value inequality:
Part (b):
Solving the inequality:
Solving the inequality:
Solution

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Mind Expander
To express the heights that do not meet the guarantee, we can formulate the absolute value inequality as follows:
This indicates that the tree’s height deviates more than 0.5 feet from the expected height of 3 feet, which means it falls outside the acceptable range.
Now, let’s solve the inequality. This leads to two separate inequalities:
-
or -
Solving these, we get:
Thus, the unacceptable heights are
or
.