# How do you solve (5x+6)/5 = (4x+10)/3?

Oct 18, 2015

$- \frac{32}{5}$

#### Explanation:

Your goal here is to isolate $x$ on one side of the equation.

To do that, start by finding the common denominator of the two fractions.

In this case, the least common multiple of $3$ and $5$ is $15$, which means that you will have to multiply the first fraction by $1 = \frac{3}{3}$ and the second fraction by $1 = \frac{5}{5}$ to get

$\frac{5 x + 6}{5} \cdot \frac{3}{3} = \frac{4 x + 10}{3} \cdot \frac{5}{5}$

$\frac{3 \left(5 x + 6\right)}{15} = \frac{5 \left(4 x + 10\right)}{15}$

At this point, you know that the equation comes down to

$3 \cdot \left(5 x + 6\right) = 5 \cdot \left(4 x + 10\right)$

Expand the parantheses and isolate $x$ on one side of the equation to get

$15 x + 18 = 20 x + 50$

$15 x - 20 x = 50 - 18$

$- 5 x = 32 \implies x = \textcolor{g r e e n}{- \frac{32}{5}}$