Solve p=5+2p/3-q

$$p = 5 + \frac { 2 p } { 3 - q }$$

Solve for p

$$p=-\frac{5\left(q-3\right)}{1-q}$$

$$q\neq 1\text{ and }q\neq 3$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{3-q}{3-q}.

$$p=\frac{5\left(3-q\right)}{3-q}+\frac{2p}{3-q}$$

Since \frac{5\left(3-q\right)}{3-q} and \frac{2p}{3-q} have the same denominator, add them by adding their numerators.

$$p=\frac{5\left(3-q\right)+2p}{3-q}$$

Do the multiplications in 5\left(3-q\right)+2p.

$$p=\frac{15-5q+2p}{3-q}$$

Subtract \frac{15-5q+2p}{3-q} from both sides.

$$p-\frac{15-5q+2p}{3-q}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply p times \frac{3-q}{3-q}.

$$\frac{p\left(3-q\right)}{3-q}-\frac{15-5q+2p}{3-q}=0$$

Since \frac{p\left(3-q\right)}{3-q} and \frac{15-5q+2p}{3-q} have the same denominator, subtract them by subtracting their numerators.

$$\frac{p\left(3-q\right)-\left(15-5q+2p\right)}{3-q}=0$$

Do the multiplications in p\left(3-q\right)-\left(15-5q+2p\right).

$$\frac{3p-pq-15+5q-2p}{3-q}=0$$

Combine like terms in 3p-pq-15+5q-2p.

$$\frac{p-pq-15+5q}{3-q}=0$$

Multiply both sides of the equation by -q+3.

$$p-pq-15+5q=0$$

Add 15 to both sides. Anything plus zero gives itself.

$$p-pq+5q=15$$

Subtract 5q from both sides.

$$p-pq=15-5q$$

Combine all terms containing p.

$$\left(1-q\right)p=15-5q$$

Divide both sides by -q+1.

$$\frac{\left(1-q\right)p}{1-q}=\frac{15-5q}{1-q}$$

Dividing by -q+1 undoes the multiplication by -q+1.

$$p=\frac{15-5q}{1-q}$$

Divide 15-5q by -q+1.

$$p=\frac{5\left(3-q\right)}{1-q}$$

Solve for q

$$q=-\frac{15-p}{p-5}$$

$$p\neq 0\text{ and }p\neq 5$$

Steps for Solving Linear Equation

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

$$p\left(-q+3\right)=\left(-q+3\right)\times 5+2p$$

Use the distributive property to multiply p by -q+3.

$$-pq+3p=\left(-q+3\right)\times 5+2p$$

Use the distributive property to multiply -q+3 by 5.

$$-pq+3p=-5q+15+2p$$

Add 5q to both sides.

$$-pq+3p+5q=15+2p$$

Subtract 3p from both sides.

$$-pq+5q=15+2p-3p$$

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

$$-pq+5q=15-p$$

Combine all terms containing q.

$$\left(-p+5\right)q=15-p$$

The equation is in standard form.

$$\left(5-p\right)q=15-p$$

Divide both sides by -p+5.

$$\frac{\left(5-p\right)q}{5-p}=\frac{15-p}{5-p}$$

Dividing by -p+5 undoes the multiplication by -p+5.

$$q=\frac{15-p}{5-p}$$

Variable q cannot be equal to 3.

$$q=\frac{15-p}{5-p}\text{, }q\neq 3$$