# What is the solution set of the equation x +7/ 2= (5x)/3?

May 5, 2018

$x = 5 \frac{1}{4}$

#### Explanation:

To solve $x + \frac{7}{2} = \frac{5 x}{3}$

Begin by multiplying all of the terms by the common denominator which is $6$

$\left(6\right) x + \left(6\right) \frac{7}{2} = \left(6\right) \frac{5 x}{3}$

$6 x + 21 = 10 x$

Now us the additive inverse to combine the variable values

$\cancel{6 x} + 21 \cancel{- 6 x} = 10 x - 6 x$

$21 = 4 x$

$\frac{21}{4} = \frac{\cancel{4} x}{\cancel{4}}$

$\frac{21}{4} = x$

$x = 5 \frac{1}{4}$