The width of a rectangle is x inches long. The length of that rectangle is 5 inches less than Twice the width. If the perimeter measures 26 inches, what is the measure of the length and width of the rectangle. Show all the work and the algebra you used to solve this problem.

If width = x, then 2x-5 = length.

2x + 2(2x-5) = 26

Solve for x.

To find the measurements of the rectangle, we need to set up equations based on the given information and then solve them algebraically.

Let's proceed step by step:

1. Let's assign variables to the width (x) and length (L) of the rectangle.

2. The length of the rectangle is stated to be 5 inches less than twice the width. Therefore, we can represent the length as L = 2x - 5.

3. The perimeter of a rectangle is the sum of all four sides. Since a rectangle has two pairs of equal sides, we can write the equation for the perimeter as:
Perimeter = 2(width) + 2(length)

Given that the perimeter measures 26 inches, we can write the equation as:
26 = 2x + 2(2x - 5)

4. Simplify and solve the equation:
26 = 2x + 4x - 10
Combine like terms:
6x - 10 = 26
Add 10 to both sides:
6x = 36
Divide both sides by 6:
x = 6

Now that we have the value of x, we can find the length by substituting x = 6 into L = 2x - 5:
L = 2(6) - 5
L = 12 - 5
L = 7

Therefore, the width of the rectangle is 6 inches, and the length is 7 inches.