Here's our equation:
[tex]\frac{1}{4} (-8x-12)-4=\frac{3}{4} (-8x-12)[/tex]
Factor out the left side
(-2x - 3) - 4 = 3/4 (-8x - 12)
Simplify
-2x - 7 = 3/4 (-8x - 12)
Factor out the right side
-2x - 7 = -6x - 9
Add 7
-2x = 6x - 2
Add 6x to isolate the variable
4x = -2
Divide by 4
x = - 1/2
Here is how I simplified both sides initially. I'll only be showing the right side because this is a LOT of typing.
Begin with 3/4 (-8x - 12)
Use rule [tex]a*\frac{b}{c} = \frac{a * b}{c}[/tex] to multiply
3(-8x-12)/4
Factor 3(-8x-12)
(-8x - 12) = (-4 * 2x - 4 * 3)
Simplify (-4 * 2x - 4 * 3)
-3 * 4 (2x+3)
- 12 (2x + 3)
Now that we've factored 3/4 (-8x - 12), we're left with- 12 (2x + 3)/4.
12/4 =3, giving us -3(2x + 3)
Distribute and simplify, then you're done.
