Solve 6=x-5/y+3

$$6 = \frac { x - 5 } { y + 3 }$$

Solve for x

$$x=6y+23$$

$$y\neq -3$$

Solution Steps

Multiply both sides of the equation by y+3.

$$6\left(y+3\right)=x-5$$

Use the distributive property to multiply 6 by y+3.

$$6y+18=x-5$$

Swap sides so that all variable terms are on the left hand side.

$$x-5=6y+18$$

Add 5 to both sides.

$$x=6y+18+5$$

Add 18 and 5 to get 23.

$$x=6y+23$$

Solve for y

$$y=\frac{x-23}{6}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Variable y cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by y+3.

$$6\left(y+3\right)=x-5$$

Use the distributive property to multiply 6 by y+3.

$$6y+18=x-5$$

Subtract 18 from both sides.

$$6y=x-5-18$$

Subtract 18 from -5 to get -23.

$$6y=x-23$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{x-23}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{x-23}{6}$$

Variable y cannot be equal to -3.

$$y=\frac{x-23}{6}\text{, }y\neq -3$$