# How do you solve 2/3x + 4 = 3/5x - 2?

Mar 10, 2018

#### Answer:

$x = - 90$

#### Explanation:

Given: $\frac{2}{3} x + 4 = \frac{3}{5} x - 2$

One way to solve this equation is to multiply the whole equation by the common denominator of the two fractions to eliminate fractions:

The least common multiple (LCM) or common denominator of $3 \text{ & } 5$:

$\text{ } 3 : 3 , 6 , 9 , 12 , \textcolor{red}{15} , 18$

$\text{ } 5 : 5 , 10 , \textcolor{red}{15} , 20$

$\frac{15}{1} \times \left(\frac{2}{3} x + 4 = \frac{3}{5} x - 2\right)$

 30/3 x + 60 = 45/5x - 30; " " 10x + 60 = 9x - 30

Move the $x ' s$ to the same side:

$\text{ "10x + 60 = " } 9 x - 30$
$\underline{+ \text{ "-9x " " = -9x " }}$
$\text{ "x + 60 = " } - 30$
ul(" " -60 = " "-60
$\text{ } x = - 90$

Check:
$\frac{2}{3} \times \left(- \frac{90}{1}\right) + 4 = \frac{3}{5} \times \left(- \frac{90}{1}\right) - 2$

$- \frac{180}{3} + 4 = - \frac{270}{5} - 2$

$- 60 + 4 = - 54 - 2$

$- 56 = - 56$ QED