Answer:
x = 12
Explanation:
Solve for x:
(-3 x)/2 - 9 = -27
Put each term in (-3 x)/2 - 9 over the common denominator 2: (-3 x)/2 - 9 = (-18)/2 - (3 x)/2:
(-18)/2 - (3 x)/2 = -27
(-18)/2 - (3 x)/2 = (-3 x - 18)/2:
(-3 x - 18)/2 = -27
Multiply both sides of (-3 x - 18)/2 = -27 by 2:
(2 (-3 x - 18))/2 = -27×2
(2 (-3 x - 18))/2 = 2/2×(-3 x - 18) = -3 x - 18:
-3 x - 18 = -27×2
2 (-27) = -54:
-3 x - 18 = -54
Add 18 to both sides:
(18 - 18) - 3 x = 18 - 54
18 - 18 = 0:
-3 x = 18 - 54
18 - 54 = -36:
-3 x = -36
Divide both sides of -3 x = -36 by -3:
(-3 x)/(-3) = (-36)/(-3)
(-3)/(-3) = 1:
x = (-36)/(-3)
The gcd of -36 and -3 is -3, so (-36)/(-3) = (-3×12)/(-3×1) = (-3)/(-3)×12 = 12:
Answer: x = 12