# How do you define a variable and write an expression for each phrase: The product of 5 less a number and 4 less than twice the same number?

May 8, 2016

$\left(x - 5\right) \times \left(2 x - 4\right)$
A different interpretation of the English could give:
$\left(5 - x\right) \left(2 x - 4\right)$

Translate the English words into maths.

#### Explanation:

Let the number that is referred to be $x$.

It at least gives us something to work with rather than just a ?.

First, put in some punctuation in the statement to make it easier to understand. The key word is 'product'.

The word 'Product' always uses 'and'
The product of 2 and 3 would be 2 x 3.

In the expression we have ....

The product of, (5 less a number) and (4 less than twice the same number)
So, two values are being multiplied and we need an expression for each value.

'5 less than a number' means a certain number, with 5 subtracted from it. ....... [like 3, is 5 less than 8] In our case $x - 5$

"Twice a number' means the number x 2, so, $2 x$

'4 less than, twice the number' is $2 x - 4$

Now write an expression for the product of the two values for which we have written expressions:

$\left(x - 5\right) \times \left(2 x - 4\right)$

This does not need to simplified, the question is answered.

[The English is not quite clear. "5 less a number could also be interpreted as a number subtracted from 5, in which case the first bracket would be $\left(5 - x\right)$.]