# How do you solve the equation 5/2(3v-4)=30?

Jun 28, 2017

$\frac{16}{3}$, or $5 \frac{1}{3}$ as a mixed fraction.

#### Explanation:

Firstly, we must remove the fraction, to make it more easier to deal with. To divide by fraction, you multiply by the inverse, i.e. $x \div \frac{a}{b} \equiv x \cdot \frac{b}{a}$, also $\frac{a}{b} \div \frac{a}{b} \equiv \frac{a}{b} \cdot \frac{b}{a} = 1$

3v-4=30(2)/5)=60/5=12

Now, we add 4 to both sides to remove the extras.
$3 v - 4 = 12$
$3 v - 4 + 4 = 12 + 4$
$3 v = 16$

Now, to get $v$ on its own, we divide both sides by 3.
$3 v = 16$
$\frac{3 v}{3} = \frac{16}{3}$
$v = \frac{16}{3} = 5 \frac{1}{3}$ (mixed fraction)