Question

Find the perimeter of a rectangle with a length of 6x+3 and a width of -2x-5.

Answer 1

The simple way of calculating a perimeter is to add all of the sides.
For a rectangle this would equal 2 x length + 2 x width
P = 2(6x + 3) + 2(-2x - 5)
= 12x + 6 - 4x - 10
= 8x - 4

At a higher level both the length and width must be greater than zero (= zero is a trivial rectangle)
6x + 3 > 0
6x > -3
x > -0.5

-2x - 5 > 0
2x + 5 < 0 (multiplying by -1 reverses the inequality)
2x < -5
x < -2.5

This rectangle cannot exist as x cannot be < -2.5 and > -0.5 at the same time!

Answer 2

L=6x+3

B=-2x-5

$\\ \rm\longmapsto Perimeter=2(L+B)$

$\\ \rm\longmapsto Perimeter=2(6x+3-2x-5)$

$\begin{gathered}\\ \rm\longmapsto Perimeter=2(4x-2)\end{gathered}\begin{gathered}\\ \rm\longmapsto Perimeter= 8x-4\end{gathered}$