# How do you solve 6n=4n+3?

Jul 27, 2016

n = 1.5

#### Explanation:

Subtract 4n from both sides of the equation, so you are left with
2n = 3 now divide both sides of the equation by 2 and you obtain
n = 3/2 (or 1.5)
In this type of problem the overall strategy is to isolate the Unknown (n in this case) on one side of the equation. The tactic is to perform the same operations on both sides of the equation ( subtracting 4n, dividing by 2) so as to maintain the equality.

Jul 27, 2016

With practise you will start to use the shortcuts and become much faster at solving this type of question.

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

#### Explanation:

$\textcolor{b l u e}{\text{Method}}$

The trick is to manipulate the equation so that you end up with just one $n$ and for it to be on one side of the $=$ and everything else on the other side.

The shortcuts people show you are just methods of jumping steps of the first principle method.

$\textcolor{R e d}{\text{I am using First Principles to move something to the other side of the =}}$

$\textcolor{p u r p \le}{\text{For add or subtract turn it into 0. Anything + 0 does not change.}}$

$\textcolor{p u r p \le}{\text{For multiply or divide turn it into 1. Anything "xx1" does not change.}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Solving your question}}$

$\textcolor{w h i t e}{.}$

Given:$\text{ "color(brown)(6n=4n+3)larr" "4n" is on the right}$

To move the $4 n$ to the left of =
Subtract $\textcolor{b l u e}{4 n}$ from both sides

$\textcolor{b r o w n}{6 n \textcolor{b l u e}{- 4 n} = 4 n \textcolor{b l u e}{- 4 n} + 3}$

$\textcolor{b r o w n}{6 n \textcolor{b l u e}{- 4 n} = \textcolor{b l u e}{0} + 3} \leftarrow \text{ it is now on the left}$

$\implies \textcolor{b r o w n}{2 n = 3}$
'............................................................................................................
To move the 2 from $2 n$ to the right
Divide both sides by $\textcolor{b l u e}{2}$

color(brown)(2/(color(blue)(2))xxn=3/(color(blue)(2))

color(brown)(color(blue)(1xx)n=3/(color(blue)(2)) larr" now it is on the right"

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