Solve y-x+1/6x=(x)

$$y - x + \frac { 1 } { 6 } x = ( x )$$

Solve for x

$$x=\frac{6y}{11}$$

Steps for Solving Linear Equation

Combine -x and \frac{1}{6}x to get -\frac{5}{6}x.

$$y-\frac{5}{6}x=x$$

Subtract x from both sides.

$$y-\frac{5}{6}x-x=0$$

Combine -\frac{5}{6}x and -x to get -\frac{11}{6}x.

$$y-\frac{11}{6}x=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$-\frac{11}{6}x=-y$$

Divide both sides of the equation by -\frac{11}{6}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{11}{6}x}{-\frac{11}{6}}=-\frac{y}{-\frac{11}{6}}$$

Dividing by -\frac{11}{6} undoes the multiplication by -\frac{11}{6}.

$$x=-\frac{y}{-\frac{11}{6}}$$

Divide -y by -\frac{11}{6} by multiplying -y by the reciprocal of -\frac{11}{6}.

$$x=\frac{6y}{11}$$

Solve for y

$$y=\frac{11x}{6}$$

Solution Steps

Combine -x and \frac{1}{6}x to get -\frac{5}{6}x.

$$y-\frac{5}{6}x=x$$

Add \frac{5}{6}x to both sides.

$$y=x+\frac{5}{6}x$$

Combine x and \frac{5}{6}x to get \frac{11}{6}x.

$$y=\frac{11}{6}x$$