# How do you solve (6/7)x - (2/3)=4 ?

Apr 17, 2018

color(maroon)(x = 5 (4/9) " or " 5.44

#### Explanation:

$\left(\frac{6}{7}\right) x - \left(\frac{2}{3}\right) = 4$

$L C M \text{ "of " } 7 , 3 = 21$

Taking 21 as L C M for L H S,

$\frac{\left(3 \cdot 6 x\right) - \left(2 \cdot 7\right)}{21} = 4$

$18 x - 14 = 4 \cdot 21 = 84 , \text{ cross multiplying}$

$18 x = 84 + 14 = 98$

$x = \frac{98}{18} = \frac{49 \cdot \cancel{2}}{9 \cdot \cancel{2}} = \frac{49}{9}$

color(maroon)(x = 5 (4/9) " or " 5.44..