A graphic artist is designing a poster to advertise a modern art exhibit. The area of the rectangular poster must be greater than 0 square inches, but no more than 96 square inches.

If the length of the poster is 12 inches, then which expression defines all the possible values for its width (w) in inches?

If the length of the (rectangular) poster is L = 12 inches, the area is

0 <= L * W = 12 * W <= 96 sq in
0 <= W <= 8 inches

To find the expression that defines all the possible values for the width (w) of the poster, we can use the formula for the area of a rectangle: Area = Length × Width.

Given that the length of the poster is 12 inches and the area must be between 0 and 96 square inches, we can set up an inequality to represent this:

0 < 12w ≤ 96

To solve this inequality, we can isolate the variable w by dividing both sides of the inequality by 12:

0/12 < w ≤ 96/12

0 < w ≤ 8

Therefore, the expression that defines all the possible values for the width (w) of the poster is 0 < w ≤ 8.