# How do you solve -2( - 11w + 17) + 2= - 5w + 4- 9w?

May 24, 2018

$w = 1$

#### Explanation:

$- 2 \left(- 11 w + 17\right) + 2 = - 5 w + 4 - 9 w$

First, distribute $- 2$ to $- 11 w$ and $17$. You do this by multiplying the numbers in the parentheses by the number on the outside. Let's make equations for this to make it easier:

$- 2 \cdot - 11 w$ = $22 w$ because two negatives create a positive.
$- 2 \cdot 17 = - 34$ because a negative times a positive will equal a negative.

Rewrite your equation since you have distributed:

$22 w - 34 + 2 = - 5 w + 4 - 9 w$

Now, combine like terms. What this means is that you'll be adding similar numbers and variables.

On the left side:
$- 34 + 2 = - 32$

On the right side:
$- 5 w - 9 w = - 14 w$ because two negatives added together continue to be negative. Think about a number line.

$22 w - 32 = - 14 w + 4$

Now, get rid of the lowest value variable. This is $- 14 w$. To cancel it out, add $- 14 w$ to both sides. You should now have:

$36 w - 32 = 4$

Now, add $32$ to both sides to cancel out $- 32$. You should now have:

$36 w = 36$

Divide by $36$ to isolate for $w$:

$w = 1$

To verify that this is right, I'll be plugging in this value:

$- 2 \left(- 11 \left(1\right) + 17\right) + 2 = - 5 \left(1\right) + 4 - 9 \left(1\right)$
$22 - 34 + 2 = - 5 + 4 - 9$
$- 10 = - 14 + 4$
$- 10 = - 10$