Solve for p p-31/6=-21/2

$p - \frac{31}{6} = - \frac{21}{2}$

Step 1

Add $\frac{31}{6}$ to both sides of the equation.

$p = - \frac{21}{2} + \frac{31}{6}$

Step 2

To write $- \frac{21}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$p = - \frac{21}{2} \cdot \frac{3}{3} + \frac{31}{6}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{21}{2}$ by $\frac{3}{3}$ .

$p = - \frac{21 \cdot 3}{2 \cdot 3} + \frac{31}{6}$

Multiply $2$ by $3$ .

$p = - \frac{21 \cdot 3}{6} + \frac{31}{6}$

Step 4

Combine the numerators over the common denominator.

$p = \frac{- 21 \cdot 3 + 31}{6}$

Step 5

Simplify the numerator.

Multiply $- 21$ by $3$ .

$p = \frac{- 63 + 31}{6}$

Add $- 63$ and $31$ .

$p = \frac{- 32}{6}$

Step 6

Cancel the common factor of $- 32$ and $6$ .

Factor $2$ out of $- 32$ .

$p = \frac{2 (- 16)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$p = \frac{2 \cdot - 16}{2 \cdot 3}$

Cancel the common factor.

$p = \frac{2 \cdot - 16}{2 \cdot 3}$

Rewrite the expression.

$p = \frac{- 16}{3}$

Step 7

Move the negative in front of the fraction.

$p = - \frac{16}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{16}{3}$

Decimal Form:

$p = - 5.\overline{3}$

Mixed Number Form:

$p = - 5 \frac{1}{3}$