Solve p+7/p-6=1/3

$$\frac { p + 7 } { p - 6 } = \frac { 1 } { 3 }$$

Solve for p

$$p = -\frac{27}{2} = -13\frac{1}{2} = -13.5$$

Steps for Solving Linear Equation

Variable p cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by 3\left(p-6\right), the least common multiple of p-6,3.

$$3\left(p+7\right)=p-6$$

Use the distributive property to multiply 3 by p+7.

$$3p+21=p-6$$

Subtract p from both sides.

$$3p+21-p=-6$$

Combine 3p and -p to get 2p.

$$2p+21=-6$$

Subtract 21 from both sides.

$$2p=-6-21$$

Subtract 21 from -6 to get -27.

$$2p=-27$$

Divide both sides by 2.

$$p=\frac{-27}{2}$$

Fraction \frac{-27}{2} can be rewritten as -\frac{27}{2} by extracting the negative sign.

$$p=-\frac{27}{2}$$