Solve (m+2/n+2=1/2

$$( \frac { m + 2 } { n + 2 } = \frac { 1 } { 2 }$$

Solve for m

$$m=\frac{n-2}{2}$$

$$n\neq -2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(n+2\right), the least common multiple of n+2,2.

$$2\left(m+2\right)=n+2$$

Use the distributive property to multiply 2 by m+2.

$$2m+4=n+2$$

Subtract 4 from both sides.

$$2m=n+2-4$$

Subtract 4 from 2 to get -2.

$$2m=n-2$$

Divide both sides by 2.

$$\frac{2m}{2}=\frac{n-2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m=\frac{n-2}{2}$$

Divide n-2 by 2.

$$m=\frac{n}{2}-1$$

Solve for n

$$n=2\left(m+1\right)$$

$$m\neq -2$$

Solution Steps

Variable n cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 2\left(n+2\right), the least common multiple of n+2,2.

$$2\left(m+2\right)=n+2$$

Use the distributive property to multiply 2 by m+2.

$$2m+4=n+2$$

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

$$n+2=2m+4$$

Subtract 2 from both sides.

$$n=2m+4-2$$

Subtract 2 from 4 to get 2.

$$n=2m+2$$

Variable n cannot be equal to -2.

$$n=2m+2\text{, }n\neq -2$$