**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]**