Question

A rectangle is 2x-3 in by 3x-1 in. Find the area.

Answer 1

`\huge\boxed{A=6x^2-11x+3;\ \text{for}\ x>1.5}`

Explanation:

The formula of an area of a rectangle:

`A=a\cdot b\\\\a,\ b-\text{sides of a rectangle}`

We have:

`a=2x-3\\b=3x-1`

The domain:

`2x-3>0\ \wedge\ 3x-1>0\\\\2x-3+3>0+3\ \wedge\ 3x-1+1>0+1\\\\2x>3\ \wedge\ 3x>1\\\\(2x)/(2)>(3)/(2)\ \wedge\ (3x)/(3)>(1)/(3)\\\\x>1.5\ \wedge\ x>(1)/(3)\Rightarrow\boxed{x>1.5}`

Substitute:

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

use FOIL: (a + b)(c + d) = ac + ad + bc + bd

`A= (2x)(3x)+(2x)(-1)+(-3)(3x)+(-3)(-1)\\\\A=6x^2-2x-9x+3`

combine like terms

`A= 6x^2+(-2x-9x)+3\\\\A=6x^2-11x+3`

Answer 2

6x² - 11x + 3

Explanation:

To find the area of a rectangle, we multiply the length by the width.

A = l • w

length: 2x-3

width: 3x-1

A = (2x-3) • (3x-1)

To multiply these two binomials, we must FOIL (first | outer | inner | last) them.

F: 2x • 3x = 6x²

O: 2x • -1 = -2x

I: -3 • 3x = -9x

L: -3 • -1 = 3

Combine the terms.

6x² - 2x - 9x + 3

Combine like terms.

6x² - 11x + 3

This is your area.

Hope this helps!