Q:  Solve for x:

-2[8 – 5(2-3x) – 7x] = 4(x – |-9|)

A:

There are many ways to start with this, so I’m just going to start on the right side of the equation first:

-2[8 – 5(2-3x) – 7x] = 4(x – |-9|)

Starting on the right (piece at a time)

We know that |-9| = 9 (by definition of absolute value), so:

4(x – |-9|)

4(x – 9)

Now use the distributive property to distribute the 4 through (multiply the 4 to the x and the 9):

4x – 36

This is the best we can do on the right side.  So the right side (for now) is 4x – 36.

Now let’s look at the left side:

-2[8 – 5(2 – 3x) – 7x]

We need to get rid of the inner most parentheses, so we should deal with the -5(2 – 3x) part.  Distribute the -5 through:

-2[8 – 10 + 15x – 7x] <– that is what happens on the left when the -5 distributed through.

Now, clean up inside the brackets and combine like terms:

-2[-2 +8x]  <— I combined the 8-10 and the 15x-7x

Now distribute the -2 through the brackets to get:

4 – 16x  <– this is as far as the left side can be simplified.  So, combining the left side = right side we get:

4 – 16x = 4x – 36

I’m going to add 16x to both sides (to get rid of the x on the left side):

4 = 20x – 36

Now add 36 to both sides:

40 = 20x

Divide both sides by 20 to get x by itself:

2 = x [final answer]