# How do you solve x/4=2+(x-3)/3?

Feb 26, 2017

$x = - 12$

#### Explanation:

$\textcolor{g r e e n}{\frac{x}{4} \textcolor{red}{\times 1} \text{ "=" } \left[2 \textcolor{red}{\times 1}\right] + \left[\frac{x - 3}{3} \textcolor{red}{\times 1}\right]}$

I chose the common denominator (bottom number) to be 12

$\textcolor{g r e e n}{\frac{x}{4} \textcolor{red}{\times \frac{3}{3}} \text{ "=" } \left[2 \textcolor{red}{\times \frac{12}{12}}\right] + \left[\frac{x - 3}{3} \textcolor{red}{\times \frac{4}{4}}\right]}$

$\textcolor{g r e e n}{\text{ "(3x)/12" "color(white)(.)=" "[24/12]color(white)(.)+" } \left[\frac{4 x - 12}{12}\right]}$

I love the one that goes: now the denominators are all the same you can forget about them.

The other one is if you are a stickler for mathematical correctness:
Multiply both sides by 12

$\textcolor{g r e e n}{3 x = 24 + 4 x - 12 \text{ "->" } 3 x = 4 x + 12}$

Subtract $3 x$ from both sides

color(green)(0=x+12

Subtract 12 from both sides

$\textcolor{g r e e n}{x = - 12}$

Feb 26, 2017

$\text{the answer is x=-12}$

#### Explanation:

$\frac{x}{4} = 2 + \frac{x - 3}{3}$

$\text{let's make equal the denominators at the right side of equation.}$

$\frac{x}{4} = \textcolor{red}{\frac{3}{3}} \cdot 2 + \frac{x - 3}{3}$

$\frac{x}{4} = \frac{6}{3} + \frac{x - 3}{3}$

$\frac{x}{4} = \frac{6 + x - 3}{3}$

$\frac{x}{4} = \frac{3 + x}{3}$

$\text{if "a/b=c/d" then } a \cdot d = b \cdot c$

$3 \cdot x = 4 \cdot \left(3 + x\right)$

$3 x = 4 \cdot 3 + 4 \cdot x$

$3 x = 12 + 4 x$

$4 x - 3 x = - 12$

$x = - 12$