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

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

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Solution Steps

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

$$2y+2-3\left(y-1\right)=5-y$$

Use the distributive property to multiply -3 by y-1.

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

Combine 2y and -3y to get -y.

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

Add 2 and 3 to get 5.

$$-y+5=5-y$$

Add y to both sides.

$$-y+5+y=5$$

Combine -y and y to get 0.

$$5=5$$

Compare 5 and 5.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for y

$$y\in \mathrm{R}$$

Solution Steps

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

$$2y+2-3\left(y-1\right)=5-y$$

Use the distributive property to multiply -3 by y-1.

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

Combine 2y and -3y to get -y.

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

Add 2 and 3 to get 5.

$$-y+5=5-y$$

Add y to both sides.

$$-y+5+y=5$$

Combine -y and y to get 0.

$$5=5$$

Compare 5 and 5.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$