Answer:
x = (-7)/5
Explanation:
Solve for x:
3 (x - 6) - 8 x = 5 (2 x + 1) - 2
3 (x - 6) = 3 x - 18:
3 x - 18 - 8 x = 5 (2 x + 1) - 2
Grouping like terms, 3 x - 8 x - 18 = (3 x - 8 x) - 18:
(3 x - 8 x) - 18 = 5 (2 x + 1) - 2
3 x - 8 x = -5 x:
-5 x - 18 = 5 (2 x + 1) - 2
5 (2 x + 1) = 10 x + 5:
-5 x - 18 = 10 x + 5 - 2
Add like terms. 5 - 2 = 3:
-5 x - 18 = 10 x + 3
Subtract 10 x from both sides:
(-5 x - 10 x) - 18 = (10 x - 10 x) + 3
-5 x - 10 x = -15 x:
-15 x - 18 = (10 x - 10 x) + 3
10 x - 10 x = 0:
-15 x - 18 = 3
Add 18 to both sides:
(18 - 18) - 15 x = 18 + 3
18 - 18 = 0:
-15 x = 3 + 18
3 + 18 = 21:
-15 x = 21
Divide both sides of -15 x = 21 by -15:
(-15 x)/(-15) = 21/(-15)
(-15)/(-15) = 1:
x = 21/(-15)
The gcd of 21 and -15 is 3, so 21/(-15) = (3×7)/(3 (-5)) = 3/3×7/(-5) = 7/(-5):
x = 7/(-5)
Multiply numerator and denominator of 7/(-5) by -1:
Answer: x = (-7)/5