To find the equation that describes the relationship between the width \( w \) of the rectangle and the area \( A \), we start by expressing the length in terms of the width.
Given that the length \( l \) is 2 inches less than 3 times the width \( w \), we can write the equation for length as:
\[ l = 3w - 2 \]
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times w \]
Substituting the expression for length into the area formula, we get:
\[ A = (3w - 2) \times w \]
This simplifies to:
\[ A = 3w^2 - 2w \]
Therefore, the equation that describes the relationship between \( w \) and \( A \) is:
\[ \boxed{A = 3w^2 - 2w} \]
This corresponds to the option:
A=3w²−2w (cap A is equal to 3 w squared minus 2 w).