The length of a rectangle is represented as l(x)= 4x-1. The width of the rectangle is represented as w(x)= 2x+3. What is the area, A(x), of the rectangle?

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The area of a rectangle is equation to its length multiplied by its width:

`A=lw`

Substituting what we know:

`A(x)=l(x)w(x)`

`A(x)=(4x-1)(2x+3)`

`=(4x)(2x)+(4x)(3)+(-1)(2x)+(-1)(3)`

`=8x^2+12x-2x-3`

`=8x^2+10x-3`

Therefore, the equation for the area of the rectangle is `8x^2+10x-3`

`A= l xx w=(4x-1)(2x+3)=8x^2+12x-2x-3=8x^2+10x-3`

The Area value graph. Note the negative value for `-3/2 <= x <= 1/4` are discarged for neagtive values for area have no meaning.

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