Solve 13/2=3(p+2)/2-2(p+1)/3

$$\frac { 13 } { 2 } = \frac { 3 ( p + 2 ) } { 2 } - \frac { 2 ( p + 1 ) } { 3 }$$

Solve for p

$$p=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$39=3\times 3\left(p+2\right)-2\times 2\left(p+1\right)$$

Multiply 3 and 3 to get 9. Multiply -2 and 2 to get -4.

$$39=9\left(p+2\right)-4\left(p+1\right)$$

Use the distributive property to multiply 9 by p+2.

$$39=9p+18-4\left(p+1\right)$$

Use the distributive property to multiply -4 by p+1.

$$39=9p+18-4p-4$$

Combine 9p and -4p to get 5p.

$$39=5p+18-4$$

Subtract 4 from 18 to get 14.

$$39=5p+14$$

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

$$5p+14=39$$

Subtract 14 from both sides.

$$5p=39-14$$

Subtract 14 from 39 to get 25.

$$5p=25$$

Divide both sides by 5.

$$p=\frac{25}{5}$$

Divide 25 by 5 to get 5.

$$p=5$$