# Seven times a number is the same as 12 more than 3 times the number. How do you find the number?

Oct 21, 2016

#### Explanation:

Make n as the unknown number.

$7 \times n = 12 + 3 \times n$

actually
$7 n = 12 + 3 n$

You can see that there are two different terms.
The terms that are alike are 7n and 3n.

You need to send either one term to the left or to the right.

I would choose the term with $n$ to go on the left-hand side.
So, I would bring $3 n$ to the left-hand side.

As you can see, $3 n$ is being added by something (always refer to this when solving this type of equation). To send it to the left-hand side, it has to become subtracted (since it's the opposite of addition) and becomes $- 3 n$ as you put it on the left.

$- 3 n + 7 n = 12$

Simplify, if possible.
There are two terms with $n$ on the right-hand side, so you have to add them up.

What is $- 3 n + 7 n$??

Yeah, it's positive $4 n$.
So now you have $4 n = 12$ left.

How do you solve $4 n = 12$ to find $n$??

As you can see, $n$ is being multiplied by 4 on the left-hand side, you want to send 4 to the right-hand side.

So what is the opposite of multiplication??
Yes! It's division.

Send $4$ to the right-hand side and it becomes divided by $12$.
$n = \frac{12}{4}$

Final step,
What is 12 divide 4?
Yeah! It's 3, huh? Easy as that.

$n = 3$

So now you've found out that the number is 3.

$7 n = 12 + 3 n$
$- 3 n + 7 n = 12$
$4 n = 12$
$n = \frac{12}{4}$
$n = 3$