Final answer:
To find the value of x for the rectangle's length, the perimeter formula 2(length + width) = 32 inches is used, whereby x is the length and 3x - 4 is the width.
Step-by-step explanation:
The length of a rectangle is represented by x. The width is given as 4 inches less than 3 times the length, which can be expressed as 3x - 4 inches. The perimeter of a rectangle is calculated by the formula 2(length + width), and for this rectangle, it is given as 32 inches. To find the value of x, we will set up an equation using the perimeter formula:
2(x + 3x - 4) = 32
Distributing the 2 gives us:
2x + 6x - 8 = 32
Combine like terms to simplify the equation:
8x - 8 = 32
Add 8 to both sides of the equation:
8x = 40
Divide by 8 to solve for x:
x = 40 / 8 = 5
Therefore, the length of the rectangle is 5 inches.