How would I solve (1)/(2) x-(5)/(3) =-(1)/(2) x+(19)/(4)?

Question

How would I solve
`(1)/(2) x-(5)/(3) =-(1)/(2) x+(19)/(4)`?

Answer 1

Best Approach would be by Multiply through by the LCM of the Denominators (2,3,4).

LCM = 12

12(½x) – (12)(5/3) = (12)(–½x) + (12)(19/4).

6x – 20 = –6x + 57

6x + 6x = 57 + 20

12x = 77

x = 77/12

Answer 2

Multiply both sides of the equation by 12. Move the variables to the left-hand side and change its sign. Move the constant to the left-hand side and change its sign. Collect like terms. Add the numbers. Divide both sides of the equation by 12.

1/2 x - 5= - 1/2 x + 19/4
6x -20= - 6x + 57
6x + 6x= 57 + 20
12x= 57 + 20
12x= 77
ANSWER
x = 77/12
Alternative Form .
x = 6 5/12, x= 6.416