Solve 2P-3/2p-3=2/5

$$\frac { 2 P - 3 } { 2 p - 3 } = \frac { 2 } { 5 }$$

Solve for P

$$P=\frac{2p}{5}+\frac{9}{10}$$

$$p\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5\left(2p-3\right), the least common multiple of 2p-3,5.

$$5\left(2P-3\right)=2\left(2p-3\right)$$

Use the distributive property to multiply 5 by 2P-3.

$$10P-15=2\left(2p-3\right)$$

Use the distributive property to multiply 2 by 2p-3.

$$10P-15=4p-6$$

Add 15 to both sides.

$$10P=4p-6+15$$

Add -6 and 15 to get 9.

$$10P=4p+9$$

Divide both sides by 10.

$$\frac{10P}{10}=\frac{4p+9}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$P=\frac{4p+9}{10}$$

Divide 4p+9 by 10.

$$P=\frac{2p}{5}+\frac{9}{10}$$

Solve for p

$$p=\frac{5P}{2}-\frac{9}{4}$$

$$P\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Variable p cannot be equal to \frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by 5\left(2p-3\right), the least common multiple of 2p-3,5.

$$5\left(2P-3\right)=2\left(2p-3\right)$$

Use the distributive property to multiply 5 by 2P-3.

$$10P-15=2\left(2p-3\right)$$

Use the distributive property to multiply 2 by 2p-3.

$$10P-15=4p-6$$

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

$$4p-6=10P-15$$

Add 6 to both sides.

$$4p=10P-15+6$$

Add -15 and 6 to get -9.

$$4p=10P-9$$

Divide both sides by 4.

$$\frac{4p}{4}=\frac{10P-9}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$p=\frac{10P-9}{4}$$

Divide 10P-9 by 4.

$$p=\frac{5P}{2}-\frac{9}{4}$$

Variable p cannot be equal to \frac{3}{2}.

$$p=\frac{5P}{2}-\frac{9}{4}\text{, }p\neq \frac{3}{2}$$