Solve (2y+1)x-5=3y-2-x

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{3}{2}=1.5\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y+1 by x.

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

Add x to both sides.

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

Combine x and x to get 2x.

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

Add 5 to both sides.

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

Add -2 and 5 to get 3.

$$2yx+2x=3y+3$$

Combine all terms containing x.

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

Divide both sides by 2y+2.

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

Dividing by 2y+2 undoes the multiplication by 2y+2.

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

Divide 3+3y by 2y+2.

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

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-1\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y+1 by x.

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

Subtract 3y from both sides.

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

Subtract x from both sides.

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

Combine -x and -x to get -2x.

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

Add 5 to both sides.

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

Add -2 and 5 to get 3.

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

Combine all terms containing y.

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

Divide both sides by -3+2x.

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

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

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

Divide 3-2x by -3+2x.

$$y=-1$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{3}{2}=1.5\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y+1 by x.

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

Add x to both sides.

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

Combine x and x to get 2x.

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

Add 5 to both sides.

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

Add -2 and 5 to get 3.

$$2yx+2x=3y+3$$

Combine all terms containing x.

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

Divide both sides by 2y+2.

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

Dividing by 2y+2 undoes the multiplication by 2y+2.

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

Divide 3+3y by 2y+2.

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

Solve for y

$$\left\{\begin{matrix}\\y=-1\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=\frac{3}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y+1 by x.

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

Subtract 3y from both sides.

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

Subtract x from both sides.

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

Combine -x and -x to get -2x.

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

Add 5 to both sides.

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

Add -2 and 5 to get 3.

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

Combine all terms containing y.

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

Divide both sides by -3+2x.

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

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

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

Divide 3-2x by -3+2x.

$$y=-1$$