Question

it seems like you might be trying to rearrange the equation. lets focus on setting up the equation for the perimeter first. the perimeter of the rectangle is given by the formula: p = 2 × (length + width) since the length is 2x − 3 and the width is x, substitute these into the perimeter formula. what equation do you get when you set the perimeter equal to 72 inches?

Explanation:

Step1: Recall the perimeter formula

The perimeter formula for a rectangle is \( P = 2\times(\text{length}+\text{width}) \).

Step2: Substitute length and width

Given length \( = 2x - 3 \) and width \( = x \), substitute into the formula: \( P = 2\times((2x - 3)+x) \).

Step3: Set \( P = 72 \)

Since the perimeter \( P \) is 72 inches, we set up the equation: \( 72 = 2\times((2x - 3)+x) \). We can also simplify the right - hand side first. Combine like terms inside the parentheses: \( (2x - 3)+x=3x - 3 \). Then the equation becomes \( 72 = 2\times(3x - 3) \), and further expanding the right - hand side gives \( 72 = 6x-6 \) (or we can keep it as \( 72 = 2((2x - 3)+x) \) before simplifying the parentheses).

Answer:

\( 72 = 2((2x - 3)+x) \) (or the simplified form \( 72=6x - 6 \))