# How do you solve 3x + \frac { 5} { 2} = 5x + \frac { 4} { 3}?

Jul 14, 2017

Collect like terms and then solve for $x$.

$x = \frac{7}{12}$

#### Explanation:

This one turns out to be fairly easy:

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

Subtract $3 x$ from both sides:

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

Subtract $\frac{4}{3}$ from both sides (and swap the sides)

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

We need a common denominator, so multiply $\frac{3}{3} \times \frac{5}{2} = \frac{15}{6}$ and $\frac{2}{2} \times - \frac{4}{3} = - \frac{8}{6}$

$2 x = \frac{15}{6} - \frac{8}{6} = \frac{7}{6}$

Now divide both sides by 2:

$x = \frac{7}{12}$

Jul 14, 2017

The answer is $\frac{7}{12}$.

#### Explanation:

First of all, you move the constant $+ \frac{5}{2}$ to the right, the same for $5 x$ but to the left (and don't forget for both to change its sign) which gives us

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

$\implies - 2 x = \frac{8}{6} - \frac{15}{6}$

$\implies - 2 x = - \frac{7}{6}$

Then to find $x$ you divide both sides by $- 2$, which gives us $\frac{7}{12}$.