Answer:
x = -6
Explanation:
Solve for x:
2 (3 x - 4) = 4 (x/2 - 8)
Put each term in x/2 - 8 over the common denominator 2: x/2 - 8 = x/2 - 16/2:
2 (3 x - 4) = 4 x/2 - 16/2
x/2 - 16/2 = (x - 16)/2:
2 (3 x - 4) = 4 (x - 16)/2
4/2 = (2×2)/2 = 2:
2 (3 x - 4) = 2 (x - 16)
Divide both sides by 2:
3 x - 4 = x - 16
Subtract x from both sides:
(3 x - x) - 4 = (x - x) - 16
3 x - x = 2 x:
2 x - 4 = (x - x) - 16
x - x = 0:
2 x - 4 = -16
Add 4 to both sides:
2 x + (4 - 4) = 4 - 16
4 - 4 = 0:
2 x = 4 - 16
4 - 16 = -12:
2 x = -12
Divide both sides of 2 x = -12 by 2:
(2 x)/2 = (-12)/2
2/2 = 1:
x = (-12)/2
The gcd of -12 and 2 is 2, so (-12)/2 = (2 (-6))/(2×1) = 2/2×-6 = -6:
Answer: x = -6