Question

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

Answer 1

Answer:

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