# How do you translate into mathematical expressions and find the number given The product of two and three less than a number is a negative four?

Jun 30, 2016

$2 \times \left(x - 3\right) = - 4$
$x = 1$

#### Explanation:

One key word in understanding this sentence is the word "AND".

A product is the answer to a multiplication. When the word 'product' is used, it will always say the product of (one number) AND (another number).

The other key word that we look for is, "IS". This indicates what the answer will be and represents an equal sign in an equation.
Use $x$ as 'the number' referred to

So. translate this English sentence as follows:

The PRODUCT of (two) AND (three less than a number) IS (negative four.)

The PRODUCT of (2) AND (3 less than $x$) IS (-4)

$2 \times \left(x - 3\right) = - 4$

Now that we have an equation we can solve it to find $x$

$2 x - 6 = - 4$

$2 x = - 4 + 6 = 2$

$2 x = 2 \Rightarrow x = 1$

Check: $2 \times \left(1 - 3\right) = 2 \times - 2 = - 4$