Question

*Write An inequality then solve for the width.* The length of a rectangle is 12 more than its width. what values of the width will make the perimeter less than 96 feet? (Will give brainliest to best answer)

Answer 1

Let $x$ be the width of the rectangle, so the length will be $12+x$.
Now, to find the perimeter of our rectangle, we are going to use the formula for the perimeter of a rectangle formula: $P=2(w+l)$
where 
$P$ is the perimeter 
$w$ is the width 
$l$ is the length 

We know that $w=x$ and $l=12+x$, so lets replace those values in our formula:
$P=2(x+12+x)$
$P=2(2x+12)$
$P=4x+24$

We want values of the width that will make the perimeter less than 96 feet, so lets set up our inequality:
$4x+24\ \textless \ 96$
$4x\ \textless \ 72$
$x\ \textless \ \frac{72}{4}$
$x\ \textless \ 18$

Since the width can't be zero, we can conclude that the values of the width that will make the perimeter less than 96 feet are: $0\ \textless \ x\ \textless \ 18$ or in interval notation: (0,18)