Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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?

1 Answer

Mar 20, 2016

Area $= 4 x^{2} - 9 x$ $=4x^2-9x$

Explanation:

We will convert the variable to include $x$ $x$ afterwards

Breaking down the question into its component parts

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

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

If x represents length $\to W = (4 \times x) - 9$ $->W=(4xxx)-9$

Width $\to W = 4 x - 9$ $->color(green)(W=4x-9)$

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

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

Substituting for width gives

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

Multiplying out the bracket gives

$A = 4 x^{2} - 9 x$ $A=4x^2-9x$

Related questions

See all questions in Variable Expressions

Impact of this question

4162 views around the world

You can reuse this answer
Creative Commons License