7 Times a number equals 3 less than 5 times that number. What is the number?

Jan 11, 2017

The number is $- \frac{3}{2}$

Explanation:

First, let's define the number we are looking for as $n$.

In mathematical terms "7 times as number" can be written as:

$7 \times n$ or $7 \cdot n$ or we will use $7 n$

In mathematical terms "3 less than 5 times that number" can be written as:

$5 n - 3$

If these two expressions are equal we can write:

$7 n = 5 n - 3$

We can now solve for $n$:

$7 n - \textcolor{red}{5 n} = 5 n - 3 - \textcolor{red}{5 n}$

$\left(7 - 5\right) n = 5 n - \textcolor{red}{5 n} - 3$

$2 n = 0 - 3$

$2 n = - 3$

$\frac{2 n}{\textcolor{red}{2}} = - \frac{3}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} n}{\cancel{\textcolor{red}{2}}} = - \frac{3}{2}$

$n = - \frac{3}{2}$