Answer:
x = 76/15
Explanation:
Solve for x:
-(3 x)/4 + 1/3 + 6 = x/2
Put each term in -(3 x)/4 + 1/3 + 6 over the common denominator 12: -(3 x)/4 + 1/3 + 6 = -(9 x)/12 + 4/12 + 72/12:
-(9 x)/12 + 4/12 + 72/12 = x/2
-(9 x)/12 + 4/12 + 72/12 = (-9 x + 4 + 72)/12:
(-9 x + 4 + 72)/12 = x/2
Grouping like terms, -9 x + 4 + 72 = (72 + 4) - 9 x:
((72 + 4) - 9 x)/12 = x/2
72 + 4 = 76:
(76 - 9 x)/12 = x/2
Multiply both sides by 12:
(12 (76 - 9 x))/12 = 6 x
(12 (76 - 9 x))/12 = 12/12×(76 - 9 x) = 76 - 9 x:
76 - 9 x = (12 x)/2
12/2 = (2×6)/2 = 6:
76 - 9 x = 6 x
Subtract 6 x from both sides:
76 + (-9 x - 6 x) = 6 x - 6 x
-9 x - 6 x = -15 x:
-15 x + 76 = 6 x - 6 x
6 x - 6 x = 0:
76 - 15 x = 0
Subtract 76 from both sides:
(76 - 76) - 15 x = -76
76 - 76 = 0:
-15 x = -76
Divide both sides of -15 x = -76 by -15:
(-15 x)/(-15) = (-76)/(-15)
(-15)/(-15) = 1:
x = (-76)/(-15)
Multiply numerator and denominator of (-76)/(-15) by -1:
Answer: x = 76/15