Question

The width of a rectangle is 9 inches less than 4 times the length. If x represents the length, how do you write an algebraic expression in terms of x that represents the area of the rectangle?

Answer 1

Area`=4x^2-9x`

Explanation:

We will convert the variable to include `x` afterwards

Breaking down the question into its component parts

Let width be `W`
Let length be `L`
Let area be `A`

The width of a rectangle `->W`
is `->W=?`
9 inches less than`->W=?-9`
4 times`->W=(4xx?)-9`
the length`->W=(4xxL)-9`

If x represents length`->W=(4xxx)-9`

Width`->color(green)(W=4x-9)`

Area is calculated by `color(green)("width")` times `color(magenta)("length")`.

In this case `A=color(green)(W)color(magenta)(x)`

Substituting for width gives

`A=color(green)((4x-9))color(magenta)(x)`

Multiplying out the bracket gives

`A=4x^2-9x`