1/9+x=5/6x-3/4
9 * 4 * 3 = 108
1 / 9 = 12 / 108
5 / 6 = 90 / 108
3 / 4 = 81 / 108
1 / 9 + x = ( 5 / 6 ) x - 3 / 4
12 / 108 + x - ( 5 / 6 ) x = - 81 / 108
6x / 6 - ( 5 / 6 ) x = - 81 / 108 - 12 / 108
( 1 / 6 ) x = - 93 / 108 Multiply both sides with 6
x = 6 * ( - 93 ) / 108
x = 6 * ( - 93 ) / ( 6 * 18 )
x = - 93 / 18
multiply each term by 108 , the LCD found also by anonymous
12 + 108x = 90x - 81
18x = -93
x = -93/18
x = -31/6
To solve the equation 1/9 + x = 5/6x - 3/4, we need to isolate the variable x on one side of the equation.
First, let's simplify the equation by finding a common denominator for the fractions. The least common denominator for the denominators of 9, 6, and 4 is 36.
Multiplying the equation through by 36 would allow us to eliminate all the denominators:
36*(1/9) + 36*x = 36*(5/6)*x - 36*(3/4)
Now, let's simplify each side of the equation:
4 + 36x = 30x - 27
Next, let's collect the x terms on one side of the equation and the constant terms on the other side:
36x - 30x = -27 - 4
6x = -31
To solve for x, divide both sides of the equation by 6:
x = -31/6
So, the solution to the equation 1/9 + x = 5/6x - 3/4 is x = -31/6.