Solve -2x_{0}+3/x=1

$$- 2 x _ { 0 } + \frac { 3 } { x } = 1$$

Solve for x

$$x=\frac{3}{2x_{0}+1}$$

$$x_{0}\neq -\frac{1}{2}$$

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 x.

$$-2x_{0}x+3=x$$

Subtract x from both sides.

$$-2x_{0}x+3-x=0$$

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

$$-2x_{0}x-x=-3$$

Combine all terms containing x.

$$\left(-2x_{0}-1\right)x=-3$$

Divide both sides by -2x_{0}-1.

$$\frac{\left(-2x_{0}-1\right)x}{-2x_{0}-1}=-\frac{3}{-2x_{0}-1}$$

Dividing by -2x_{0}-1 undoes the multiplication by -2x_{0}-1.

$$x=-\frac{3}{-2x_{0}-1}$$

Divide -3 by -2x_{0}-1.

$$x=\frac{3}{2x_{0}+1}$$

Variable x cannot be equal to 0.

$$x=\frac{3}{2x_{0}+1}\text{, }x\neq 0$$

Solve for x_0

$$x_{0}=-\frac{1}{2}+\frac{3}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$-2x_{0}x+3=x$$

Subtract 3 from both sides.

$$-2x_{0}x=x-3$$

The equation is in standard form.

$$\left(-2x\right)x_{0}=x-3$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)x_{0}}{-2x}=\frac{x-3}{-2x}$$

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

$$x_{0}=\frac{x-3}{-2x}$$

Divide x-3 by -2x.

$$x_{0}=-\frac{1}{2}+\frac{3}{2x}$$