Answer
$x=3$
Work Step by Step
$\frac{3x}{4} - \frac{x}{3} + 1 = \frac{4x}{5} - \frac{3}{20}$
Subtract 1 from both sides:
$\frac{3x}{4} - \frac{x}{3} + 1 -1= \frac{4x}{5} - \frac{3}{20} - 1$
$\frac{3x}{4} - \frac{x}{3} = \frac{4x}{5} - \frac{3}{20} - 1$
$\frac{3x}{4} - \frac{x}{3} = \frac{4x}{5} - \frac{3}{20} - \frac{20}{20}$
$\frac{3x}{4} - \frac{x}{3} = \frac{4x}{5} - \frac{23}{20}$
Subtract $\frac{4x}{5}$ from both sides:
$\frac{3x}{4} - \frac{x}{3} - \frac{4x}{5}= \frac{4x}{5}- \frac{4x}{5} - \frac{23}{20}$
$\frac{3x}{4} - \frac{x}{3} - \frac{4x}{5} = - \frac{23}{20}$
Simplify by multiplying the whole equation with the least common denominator:
4 : 2 x 2
3 : 3
5 : 5
20 : 2 x 2 x 5
Hence, the LCD would be 2 x 2 x 5 x 3 = 60
$(\frac{3x}{4} - \frac{x}{3} - \frac{4x}{5})\times60 = - (\frac{23}{20})\times60$
$45x - 20x - 48x = - 69$
Simplify:
$-23x = -69$
Divide both sides by -23:
$x = 3$
