Solve x=3y+1/2y-5

$$x = \frac { 3 y + 1 } { 2 y - 5 }$$

Solve for y

$$y=\frac{5x+1}{2x-3}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Variable y cannot be equal to \frac{5}{2} since division by zero is not defined. Multiply both sides of the equation by 2y-5.

$$x\left(2y-5\right)=3y+1$$

Use the distributive property to multiply x by 2y-5.

$$2xy-5x=3y+1$$

Subtract 3y from both sides.

$$2xy-5x-3y=1$$

Add 5x to both sides.

$$2xy-3y=1+5x$$

Combine all terms containing y.

$$\left(2x-3\right)y=1+5x$$

The equation is in standard form.

$$\left(2x-3\right)y=5x+1$$

Divide both sides by 2x-3.

$$\frac{\left(2x-3\right)y}{2x-3}=\frac{5x+1}{2x-3}$$

Dividing by 2x-3 undoes the multiplication by 2x-3.

$$y=\frac{5x+1}{2x-3}$$

Variable y cannot be equal to \frac{5}{2}.

$$y=\frac{5x+1}{2x-3}\text{, }y\neq \frac{5}{2}$$

Solve for x

$$x=\frac{3y+1}{2y-5}$$

$$y\neq \frac{5}{2}$$