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

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

Solve for x

$$x=-\frac{6\left(y-1\right)}{4y-1}$$

$$y\neq \frac{1}{4}$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+3.

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

Use the distributive property to multiply y by 2x+3.

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

Subtract \frac{1}{2}x from both sides.

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

Subtract 3y from both sides.

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

Combine all terms containing x.

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

Divide both sides by 2y-\frac{1}{2}.

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

Dividing by 2y-\frac{1}{2} undoes the multiplication by 2y-\frac{1}{2}.

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

Divide 3-3y by 2y-\frac{1}{2}.

$$x=\frac{6\left(1-y\right)}{4y-1}$$

Variable x cannot be equal to -\frac{3}{2}.

$$x=\frac{6\left(1-y\right)}{4y-1}\text{, }x\neq -\frac{3}{2}$$

Solve for y

$$y=\frac{x+6}{2\left(2x+3\right)}$$

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