Answer:
x = 8
Step-by-step explanation:
Solve for x:
-2 x + 16 = 4 (x/4 - 2)
Put each term in x/4 - 2 over the common denominator 4: x/4 - 2 = x/4 - 8/4:
-2 x + 16 = 4 (x/4 - 8/4)
x/4 - 8/4 = (x - 8)/4:
-2 x + 16 = 4 ((x - 8)/4)
(4 (x - 8))/4 = 4/4×(x - 8) = x - 8:
-2 x + 16 = x - 8
Subtract x from both sides:
(-2 x - x) + 16 = (x - x) - 8
-2 x - x = -3 x:
-3 x + 16 = (x - x) - 8
x - x = 0:
-3 x + 16 = -8
Subtract 16 from both sides:
(16 - 16) - 3 x = -16 - 8
16 - 16 = 0:
-3 x = -16 - 8
-16 - 8 = -24:
-3 x = -24
Divide both sides of -3 x = -24 by -3:
(-3 x)/(-3) = (-24)/(-3)
(-3)/(-3) = 1:
x = (-24)/(-3)
The gcd of -24 and -3 is -3, so (-24)/(-3) = (-3×8)/(-3×1) = (-3)/(-3)×8 = 8:
Answer: x = 8
