Answer:
x = -1
Explanation:
Solve for x:
-13 = 5 (4 x + 1) - 2 x
5 (4 x + 1) = 20 x + 5:
-13 = 20 x + 5 - 2 x
Grouping like terms, 20 x - 2 x + 5 = (-2 x + 20 x) + 5:
-13 = (-2 x + 20 x) + 5
20 x - 2 x = 18 x:
-13 = 18 x + 5
-13 = 18 x + 5 is equivalent to 18 x + 5 = -13:
18 x + 5 = -13
Subtract 5 from both sides:
18 x + (5 - 5) = -5 - 13
5 - 5 = 0:
18 x = -5 - 13
-5 - 13 = -18:
18 x = -18
Divide both sides of 18 x = -18 by 18:
(18 x)/18 = (-18)/18
18/18 = 1:
x = (-18)/18
The gcd of -18 and 18 is 18, so (-18)/18 = (18 (-1))/(18×1) = 18/18×-1 = -1:
Answer: x = -1