#-2(-11w + 17) + 2 = -5w + 4 -9w#

First, distribute #-2# to #-11w# 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 * -11w# = #22w# because two negatives create a positive.

#-2 * 17 = -34# because a negative times a positive will equal a negative.

Rewrite your equation since you have distributed:

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

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:

#-5w - 9w = -14w# because two negatives added together continue to be negative. Think about a number line.

Now, rewrite your equation again:

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

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

#36w - 32 = 4#

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

#36w = 36#

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

#w = 1#

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

#-2(-11(1) + 17) + 2 = -5(1) + 4 -9(1)#

#22 - 34 + 2 = -5 + 4 - 9#

#-10 = -14 + 4#

#-10 = -10#