# How do you solve 3v+5-7v+18=17?

Jan 21, 2015

We want to have all the terms involving $v$ on one side, and all the known numbers on the other side.

To do so, begin with subtracting 18 from both sides:
3v+5−7v+18-18=17-18, which yields
3v+5−7v=-1

Then, subtract 5 from both sides:
3v+5−7v-5=-1-5, which yields
3v−7v=-6

Now we compute $3 v - 7 v = v \left(3 - 7\right) = - 4 v$

We have finally reached the form
$- 4 v = - 6$, which means that we have all terms involving the variable $v$ on the left and all known numbers on the right.

We can divide by 4 on both sides, and get
$- v = - \setminus \frac{6}{4} = - \setminus \frac{3}{2}$
and finally deduct $v = \setminus \frac{3}{2}$.