Answer:
(0, 7]
Step-by-step explanation:
Let's call the width W and the length L. The length is 18 feet more than the width, so:
L = W + 18
The area can be no more than 175, so:
A ≤ 175
LW ≤ 175
Since L = W + 18:
(W + 18) W ≤ 175
W² + 18W ≤ 175
W² + 18W - 175 ≤ 0
(W - 7) (W + 25) ≤ 0
-25 ≤ W ≤ 7
However, the width of the table can't be nonpositive, so:
0 < W ≤ 7
Or in interval notation, (0, 7].
