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]