Answer:
x = -5
Explanation:
Solve for x:
5 (-8 x - 2) - 5 (1 - 5 x) = -4 x - 8 x
-5 (1 - 5 x) = 25 x - 5:
25 x - 5 + 5 (-8 x - 2) = -4 x - 8 x
5 (-8 x - 2) = -40 x - 10:
25 x + -40 x - 10 - 5 = -4 x - 8 x
Grouping like terms, 25 x - 40 x - 10 - 5 = (25 x - 40 x) + (-5 - 10):
(25 x - 40 x) + (-5 - 10) = -4 x - 8 x
25 x - 40 x = -15 x:
-15 x + (-5 - 10) = -4 x - 8 x
-5 - 10 = -15:
-15 - 15 x = -4 x - 8 x
-4 x - 8 x = -12 x:
-15 x - 15 = -12 x
Add 12 x to both sides:
12 x - 15 x - 15 = 12 x - 12 x
12 x - 12 x = 0:
12 x - 15 x - 15 = 0
12 x - 15 x = -3 x:
-3 x - 15 = 0
Add 15 to both sides:
(15 - 15) - 3 x = 15
15 - 15 = 0:
-3 x = 15
Divide both sides of -3 x = 15 by -3:
(-3 x)/(-3) = 15/(-3)
(-3)/(-3) = 1:
x = 15/(-3)
The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):
x = 5/(-1)
Multiply numerator and denominator of 5/(-1) by -1:
Answer: x = -5