Solve m-2/3=3+n/5

$$\frac { m - 2 } { 3 } = \frac { 3 + n } { 5 }$$

Solve for m

$$m=\frac{3n+19}{5}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(m-2\right)=3\left(3+n\right)$$

Use the distributive property to multiply 5 by m-2.

$$5m-10=3\left(3+n\right)$$

Use the distributive property to multiply 3 by 3+n.

$$5m-10=9+3n$$

Add 10 to both sides.

$$5m=9+3n+10$$

Add 9 and 10 to get 19.

$$5m=19+3n$$

The equation is in standard form.

$$5m=3n+19$$

Divide both sides by 5.

$$\frac{5m}{5}=\frac{3n+19}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$m=\frac{3n+19}{5}$$

Solve for n

$$n=\frac{5m-19}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(m-2\right)=3\left(3+n\right)$$

Use the distributive property to multiply 5 by m-2.

$$5m-10=3\left(3+n\right)$$

Use the distributive property to multiply 3 by 3+n.

$$5m-10=9+3n$$

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

$$9+3n=5m-10$$

Subtract 9 from both sides.

$$3n=5m-10-9$$

Subtract 9 from -10 to get -19.

$$3n=5m-19$$

Divide both sides by 3.

$$\frac{3n}{3}=\frac{5m-19}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$n=\frac{5m-19}{3}$$