# How do you solve 3/4x-4/9=7/18x-2/3?

Mar 5, 2017

x=color(green)(-8/13

#### Explanation:

$\frac{3}{4} x - \frac{4}{9} = \frac{7}{18} x - \frac{2}{3}$

$\therefore \frac{27 x - 16 = 14 x - 24}{\textcolor{g r e e n}{36}}$

$\therefore \frac{27 x}{\textcolor{g r e e n}{36}} - \frac{16}{\textcolor{g r e e n}{36}} = \frac{14 x}{\textcolor{g r e e n}{36}} - \frac{24}{\textcolor{g r e e n}{36}}$

multiply L.H.S and R.H.S. by color(green)(36

$\therefore 27 x - 16 = 14 x - 24$

$\therefore 27 x - 14 x = - 24 + 16$

$13 x = - 8$

:.color(green)(x=-8/13

check:

substitute color(green)(x=-8/13

$\therefore \frac{3}{4} \left(\textcolor{g r e e n}{- \frac{8}{13}}\right) - \frac{4}{9} = \frac{7}{18} \left(\textcolor{g r e e n}{- \frac{8}{13}}\right) - \frac{2}{3}$

$\therefore - \frac{24}{52} - \frac{4}{9} = - \frac{56}{234} - \frac{2}{3}$

$\therefore \frac{- 108 - 104 = - 56 - 156}{\textcolor{g r e e n}{234}}$

$\therefore - \frac{108}{\textcolor{g r e e n}{234}} - \frac{104}{\textcolor{g r e e n}{234}} = - \frac{56}{\textcolor{g r e e n}{234}} - \frac{156}{\textcolor{g r e e n}{234}}$

multiply L.H.S and R.H.S. by$\textcolor{g r e e n}{234}$

$\therefore - 108 - 104 = - 56 - 156$

$\therefore - 212 = - 212$