# How do you solve \frac { - 2x } { 3} = \frac { - 5} { 2} + \frac { - x + 1} { 3}?

Mar 3, 2017

I gor $x = \frac{13}{2}$

#### Explanation:

I would first take a common denominator such as $6$ and change the numerator accordingly to get:
$\frac{2 \cdot \left(- 2 x\right)}{6} = \frac{3 \cdot \left(- 5\right) + 2 \left(- x + 1\right)}{6}$
get rid of the denominators:
$\frac{2 \cdot \left(- 2 x\right)}{\cancel{6}} = \frac{3 \cdot \left(- 5\right) + 2 \left(- x + 1\right)}{\cancel{6}}$
rearrange and solve for $x$:
$- 4 x = - 15 - 2 x + 2$
$2 x = 13$
$x = \frac{13}{2}$

Mar 3, 2017

$x = 6 \frac{1}{2}$

#### Explanation:

$\frac{- 2 x}{3} = - \frac{5}{2} + \frac{- x + 1}{3}$

$\therefore \frac{- 4 x = - 15 + 2 \left(- x + 1\right)}{6}$

$\therefore - 4 x = - 15 - 2 x + 2$

$\therefore - 4 x + 2 x = - 15 + 2$

$\therefore - 2 x = - 13$

$\therefore - x = - \frac{13}{2}$

multiply L.H.S and R.H.S. by$\textcolor{red}{-} \textcolor{red}{1}$

$\therefore \textcolor{red}{x} \textcolor{red}{=} \frac{\textcolor{red}{13}}{\textcolor{red}{2}}$

$\therefore \textcolor{red}{x} \textcolor{red}{=} \textcolor{red}{6} \frac{\textcolor{red}{1}}{\textcolor{red}{2}}$

substitute $\textcolor{red}{x} \textcolor{red}{=} \frac{\textcolor{red}{13}}{\textcolor{red}{2}}$

$\therefore \frac{- 2 \left(\frac{\textcolor{red}{13}}{\textcolor{red}{2}}\right)}{3} = - \frac{5}{2} + \frac{- \left(\frac{\textcolor{red}{13}}{\textcolor{red}{2}}\right) + 1}{3}$

$\therefore \frac{- \frac{26}{2}}{3} = - \frac{5}{2} + \frac{\left(\textcolor{red}{-} \frac{\textcolor{red}{13}}{\textcolor{red}{2}}\right) + 1}{3}$

$\therefore - {\cancel{26}}^{13} / {\cancel{2}}^{1} \times \frac{1}{3} = - \frac{5}{2} + \frac{- 6 \frac{1}{2} + 1}{3}$

$\therefore - \frac{13}{3} = - \frac{5}{2} + \frac{- 5 \frac{1}{2}}{3}$

$\therefore - \frac{13}{3} = - \frac{5}{2} + \left(\frac{- \frac{11}{2}}{3}\right)$

$\therefore - \frac{13}{3} = - \frac{5}{2} + \left(- \frac{11}{2} \times \frac{1}{3}\right)$

$\therefore - \frac{13}{3} = - \frac{5}{2} - \frac{11}{6}$

$\therefore - \frac{13}{3} = \frac{- 15 - 11}{6}$

$\therefore - \frac{13}{3} = - {\cancel{26}}^{13} / {\cancel{6}}^{3}$
$\therefore - \frac{13}{3} = - \frac{13}{3}$

Mar 3, 2017

$x = \frac{13}{2}$

#### Explanation:

$\frac{- 2 x}{3} = \frac{- 5}{2} + \frac{- x + 1}{3}$

When you have an equation with fractions you can get rid of the denominators by multiplying each term by the LCM of the denominators. In this case it is $6$

$\frac{- 2 x \times \textcolor{b l u e}{6}}{3} = \frac{- 5 \times \textcolor{b l u e}{6}}{2} + \frac{\textcolor{b l u e}{6 \times} \left(- x + 1\right)}{3}$

cancel the denominators

$\frac{- 2 x \times \textcolor{b l u e}{{\cancel{6}}^{2}}}{\cancel{3}} = \frac{- 5 \times \textcolor{b l u e}{{\cancel{6}}^{3}}}{\cancel{2}} + \frac{\textcolor{b l u e}{{\cancel{6}}^{2}} \left(- x + 1\right)}{\cancel{3}}$

$- 4 x = - 15 + 2 \left(- x + 1\right)$

$- 4 x = - 15 - 2 x + 2$

$15 - 2 = 4 x - 2 x$

$13 = 2 x$

$x = \frac{13}{2}$