Solve for x:
6-7 x+3 (2 x-8) = 20-5 (4-2 x)-x
3 (2 x-8) = 6 x-24:
6 x-24-7 x+6 = 20-5 (4-2 x)-x
Grouping like terms, 6 x-7 x-24+6 = (6 x-7 x)+(6-24):
(6 x-7 x)+(6-24) = 20-5 (4-2 x)-x
6 x-7 x = -x:
-x+(6-24) = 20-5 (4-2 x)-x
6-24 = -18:
-18-x = 20-5 (4-2 x)-x
-5 (4-2 x) = 10 x-20:
-x-18 = 20+10 x-20-x
Grouping like terms, 20-20+10 x-x = (10 x-x)+(20-20):
-x-18 = (10 x-x)+(20-20)
10 x-x = 9 x:
-x-18 = 9 x+(20-20)
20-20 = 0:
-x-18 = 9 x
Subtract 9 x from both sides:
(-x-9 x)-18 = 9 x-9 x
-x-9 x = -10 x:
-10 x-18 = 9 x-9 x
9 x-9 x = 0:
-10 x-18 = 0
Add 18 to both sides:
(18-18)-10 x = 18
18-18 = 0:
-10 x = 18
Divide both sides of -10 x = 18 by -10:
(-10 x)/(-10) = 18/(-10)
(-10)/(-10) = 1:
x = 18/(-10)
The gcd of 18 and -10 is 2, so 18/(-10) = (2×9)/(2 (-5)) = 2/2×9/(-5) = 9/(-5):
x = 9/(-5)
Multiply numerator and denominator of 9/(-5) by -1:
Answer: |x = (-9)/5
