Solve 3/2x-3y=5

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

Solve for x

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

$$y\neq -\frac{5}{3}$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x.

$$3-3y\times 2x=10x$$

Multiply -3 and 2 to get -6.

$$3-6yx=10x$$

Subtract 10x from both sides.

$$3-6yx-10x=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-6yx-10x=-3$$

Combine all terms containing x.

$$\left(-6y-10\right)x=-3$$

Divide both sides by -6y-10.

$$\frac{\left(-6y-10\right)x}{-6y-10}=-\frac{3}{-6y-10}$$

Dividing by -6y-10 undoes the multiplication by -6y-10.

$$x=-\frac{3}{-6y-10}$$

Divide -3 by -6y-10.

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

Variable x cannot be equal to 0.

$$x=\frac{3}{2\left(3y+5\right)}\text{, }x\neq 0$$

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x.

$$3-3y\times 2x=10x$$

Multiply -3 and 2 to get -6.

$$3-6yx=10x$$

Subtract 3 from both sides.

$$-6yx=10x-3$$

The equation is in standard form.

$$\left(-6x\right)y=10x-3$$

Divide both sides by -6x.

$$\frac{\left(-6x\right)y}{-6x}=\frac{10x-3}{-6x}$$

Dividing by -6x undoes the multiplication by -6x.

$$y=\frac{10x-3}{-6x}$$

Divide 10x-3 by -6x.

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