# How do you solve 2n+12=5n ?

Nov 19, 2015

Following basic rules for manipulating equations, you get
$n = 4$

#### Explanation:

Given any equation, here are some things you can do to both sides that will keep the equation valid:

• add or subtract the same amount to/from both sides
• multiply both sides by the same amount
• divide both sides by the same amount if the amount is not $0$
• exchange the two sides

Given the above rules:
We can subtract $2 n$ from both sides of $2 n + 12 = 5 n$
to get
$\textcolor{w h i t e}{\text{XXX}} 12 = 3 n$

We can exchange the sides of $12 = 3 n$
to get
$\textcolor{w h i t e}{\text{XXX}} 3 n = 12$

We can divide both sides of $3 n = 12$ by $3$
to get
$\textcolor{w h i t e}{\text{XXX}} n = 4$