6-3/4x+1/3=1/2x + what is this

x = 76/15

Step-by-step 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