Solve y=4x-3/2x+5

$$y = \frac { 4 x - 3 } { 2 x + 5 }$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

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

$$y\left(2x+5\right)=4x-3$$

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

$$2yx+5y=4x-3$$

Subtract 4x from both sides.

$$2yx+5y-4x=-3$$

Subtract 5y from both sides.

$$2yx-4x=-3-5y$$

Combine all terms containing x.

$$\left(2y-4\right)x=-3-5y$$

The equation is in standard form.

$$\left(2y-4\right)x=-5y-3$$

Divide both sides by 2y-4.

$$\frac{\left(2y-4\right)x}{2y-4}=\frac{-5y-3}{2y-4}$$

Dividing by 2y-4 undoes the multiplication by 2y-4.

$$x=\frac{-5y-3}{2y-4}$$

Divide -3-5y by 2y-4.

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

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

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

Solve for y

$$y=-\frac{3-4x}{2x+5}$$

$$x\neq -\frac{5}{2}$$