# How do you solve 2x + 31= - 7( 1- 3x )?

Oct 6, 2016

$x = 2$

#### Explanation:

You are given: $2 x + 31 = - 7 \left(1 - 3 x\right)$

Use the distributive property to distribute the $- 7$ to $\left(1 - 3 x\right)$. The equation should end up looking like this:

$2 x + 31 = - 7 \left(1 - 3 x\right)$
$2 x + 31 = \left(- 7\right) \left(1\right) - \left(- 7\right) \left(3 x\right)$
$2 x + 31 = - 7 + 21 x$

Next, you want to get all of the variables $\left(x\right)$ on one side of the equation, and all of the number part on the other side. First subtract $- 7$ from both sides; then subtract $2 x$ from both sides.

$2 x + 31 = - 7 + 21 x$
$2 x - \left(2 x\right) + 31 - \left(- 7\right) = - 7 - \left(- 7\right) + 21 x - \left(2 x\right)$
$\cancel{2 x - \left(2 x\right)} + 31 - \left(- 7\right) = \cancel{- 7 - \left(- 7\right)} + 21 x - \left(2 x\right)$

After simplifying, you should be left with:
$38 = 19 x$

Divide both sides by $19$ to get $x$ by itself.
$\frac{38}{19} = \frac{19 x}{19}$
$2 = x$