The length of a rectangle is 3 less than twice the width. Write a function rule for the perimeter in terms of w, the width

let's translate this word problem into math

the length (L) is (=) 3 less than (-3) twice the width (2*W).

L=-3+2W

we want to find the perimiter

the perimiter, P is P=2 (L+W)

if we subsitute - 3+2W for L from our first equation into our perimiter equation, we get

P=2 (-3+2W+W)

P=2 (-3+3W)

P=-6+6W

P=6W-6

so P (W) = 6W-6 is the function of the perimiter in terms of the width

l = 2w-3

P = 2 (l+w)

substitute in for l

P = 2 (2w-3 + w)

combine like terms

P = 2 (3w-3)

P = 6w-6

P (w) = 6 (w-1)