First, on each side of the equation, combine and group like terms:
-8x - 1 + x = 12 - 6x - 2−8x−1+x=12−6x−2
-8x + x - 1 = 12 - 2 - 6x−8x+x−1=12−2−6x
-8x + 1x - 1 = 12 - 2 - 6x−8x+1x−1=12−2−6x
(-8 + 1)x - 1 = (12 - 2) - 6x(−8+1)x−1=(12−2)−6x
-7x - 1 = 10 - 6x−7x−1=10−6x
Next, add color(red)(7x)7x and subtract color(blue)(10)10 from each side of the equation to solve for xx while keeping the equation balanced:
-7x - 1 + color(red)(7x) - color(blue)(10) = 10 - 6x + color(red)(7x) - color(blue)(10)−7x−1+7x−10=10−6x+7x−10
-7x + color(red)(7x) - 1 - color(blue)(10) = 10 - color(blue)(10) - 6x + color(red)(7x)−7x+7x−1−10=10−10−6x+7x
0 - 11 = 0 + (-6 + color(red)(7))x0−11=0+(−6+7)x
-11 = 1x−11=1x
-11 = x−11=x
x = -11x=−11
