The perimeter of a rectangle is 18x - 24 and the width is

2x - 9. What is the length?

A: - 7x + 3

B: 16x + 15

C: 7x - 3

D: 7x + 3

C: 7x - 3

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2 (l+w) where l is the length and w is the width

We know the perimeter is 18x - 24 and the width is 2x-9. Substituting these values into the equation

18x-24 = 2 (l+2x-9)

Divide each side by 2

(18x-24) / 2 = 2/2 (l+2x-9)

9x-12 = l+2x-9

Add 9 to each side

9x-12 + 9 = l+2x-9+9

9x - 3 = l+2x

Subtract 2x from each side

9x-2x-3 = l+2x-2x

7x - 3 = l

The length is 7x-3

C

Step-by-step explanation:

18x - 24 = 2 [length + 2x - 9]

9x - 12 = length + 2x - 9

Length = 7x - 3