# How doy ou solve 2v - 4+ 2( 4v + 6) = - 2( v + 5)?

Sep 24, 2016

$v = - \frac{3}{2}$

#### Explanation:

$2 v - 4 + 2 \left(4 v + 6\right) = - 2 \left(v + 5\right)$

First step: expand brackets - you do this by multiplying the number in front of the brackets by each of the numbers in the brackets.

$2 v - 4 + 2 \left(4 v\right) + 2 \left(6\right) = - 2 \left(v\right) - 2 \left(5\right)$
$2 v - 4 + 8 v + 12 = - 2 v - 10$

Second step: move all letters on one side and all numbers on the other side.
Note: when moving numbers/letters on the opposite side of the equal sign, you have to change signs ie. $2 v = - 1 v + 3$ would turn into 2v + 1v = 3
Also note: it doesn't matter what side you move the letters and numbers, as long as they are both on different sides.

$2 v + 8 v + 2 v = - 10 + 4 - 12$

Third step: simplify both sides.

$12 v = - 18$

Fourth step: isolate v by dividing 12 onto the opposite side. We divide because the opposite of multiply is divide and 12 is multiplied by v.

$v = - \frac{18}{12}$

Fifth step: simplify further or leave as above.

$v = - \frac{3}{2}$

To get -3 and 2, I divided -18 and 12 by the highest common factor which was 6.