# How do you solve 2(1-2x)/3 -2x = -2/5 + 4(2-3x)/3?

Feb 28, 2016

$x = - \frac{28}{25} \to - 1 \frac{3}{25}$

#### Explanation:

Given:$\textcolor{b r o w n}{\text{ } 2 \frac{1 - 2 x}{3} - 2 x = - \frac{2}{5} + 4 \frac{2 - 3 x}{3}}$...(2)

'~~~~~~~~~~~Looking at the left hand side ~~~~~~~~~~~~~~~~~~~~~

Consider: $2 \frac{1 - 2 x}{3} \text{ " ->" " 2+(1-2x)/3" " ->" } \textcolor{g r e e n}{\frac{6}{3} + \frac{1 - 2 x}{3}}$

Consider:$\text{ "-2x" "->" } \textcolor{g r e e n}{\frac{- 6 x}{3}}$

So the left hand side becomes
$\frac{6}{3} + \frac{1 - 2 x}{3} - \frac{6 x}{3}$

$\frac{6 + 1 - 2 x - 6 x}{3}$

$\textcolor{g r e e n}{\frac{7 - 8 x}{3}}$

'~~~~~~~~~~Looking at the right hand side ~~~~~~~~~~~~~~~~~~~~~

Using the same method as above

Consider:$\text{ "4 (2-3x)/3" " -> (12+2-3x)/3" } \to \frac{14 - 3 x}{3}$

Consider:$\text{ } - \frac{2}{5}$ The denominator is not 3

So all the RHS is

$\text{ "-2/5+(14-3x)/3" " -> (-6+70-15x)/15} \to \textcolor{g r e e n}{\frac{63 - 15 x}{15}}$

'~~~~~~~~~~Putting both sides together~~~~~~~~~~~~~~~~~~~~

$\textcolor{g r e e n}{\frac{7 - 8 x}{3}} = \textcolor{g r e e n}{\frac{63 - 15 x}{15}}$

Making the denominators the same gives

$\frac{35 - 40 x}{15} = \frac{63 - 15 x}{15}$

Thus:

$35 - 40 x = 63 - 15 x$

$40 x - 15 x = 35 - 63$

$25 x = - 28$

$x = - \frac{28}{25} \to - 1 \frac{3}{25}$