Solve for p -3/8p+1/2+5/4p=-1/2p-2+7/8p

$- \frac{3}{8} p + \frac{1}{2} + \frac{5}{4} p = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Simplify $- \frac{3}{8} p + \frac{1}{2} + \frac{5}{4} p$ .

Simplify each term.

Combine $p$ and $\frac{3}{8}$ .

$- \frac{p \cdot 3}{8} + \frac{1}{2} + \frac{5}{4} p = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Move $3$ to the left of $p$ .

$- \frac{3 \cdot p}{8} + \frac{1}{2} + \frac{5}{4} p = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Combine $\frac{5}{4}$ and $p$ .

$- \frac{3 p}{8} + \frac{1}{2} + \frac{5 p}{4} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

To write $\frac{5 p}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{3 p}{8} + \frac{5 p}{4} \cdot \frac{2}{2} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 p}{4}$ by $\frac{2}{2}$ .

$- \frac{3 p}{8} + \frac{5 p \cdot 2}{4 \cdot 2} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Multiply $4$ by $2$ .

$- \frac{3 p}{8} + \frac{5 p \cdot 2}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Combine the numerators over the common denominator.

$\frac{- 3 p + 5 p \cdot 2}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Simplify each term.

Simplify the numerator.

Factor $p$ out of $- 3 p + 5 p \cdot 2$ .

Factor $p$ out of $- 3 p$ .

$\frac{p \cdot - 3 + 5 p \cdot 2}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Factor $p$ out of $5 p \cdot 2$ .

$\frac{p \cdot - 3 + p (5 \cdot 2)}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Factor $p$ out of $p \cdot - 3 + p (5 \cdot 2)$ .

$\frac{p (- 3 + 5 \cdot 2)}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Multiply $5$ by $2$ .

$\frac{p (- 3 + 10)}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Add $- 3$ and $10$ .

$\frac{p \cdot 7}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Move $7$ to the left of $p$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{1}{2} p - 2 + \frac{7}{8} p$

Simplify $- \frac{1}{2} p - 2 + \frac{7}{8} p$ .

Simplify each term.

Combine $p$ and $\frac{1}{2}$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{p}{2} - 2 + \frac{7}{8} p$

Combine $\frac{7}{8}$ and $p$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{p}{2} - 2 + \frac{7 p}{8}$

To write $- \frac{p}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{p}{2} \cdot \frac{4}{4} + \frac{7 p}{8} - 2$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{p}{2}$ by $\frac{4}{4}$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{p \cdot 4}{2 \cdot 4} + \frac{7 p}{8} - 2$

Multiply $2$ by $4$ .

$\frac{7 p}{8} + \frac{1}{2} = - \frac{p \cdot 4}{8} + \frac{7 p}{8} - 2$

Combine the numerators over the common denominator.

$\frac{7 p}{8} + \frac{1}{2} = \frac{- p \cdot 4 + 7 p}{8} - 2$

Simplify each term.

Simplify the numerator.

Factor $p$ out of $- p \cdot 4 + 7 p$ .

Factor $p$ out of $- p \cdot 4$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{p (- 1 \cdot 4) + 7 p}{8} - 2$

Factor $p$ out of $7 p$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{p (- 1 \cdot 4) + p \cdot 7}{8} - 2$

Factor $p$ out of $p (- 1 \cdot 4) + p \cdot 7$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{p (- 1 \cdot 4 + 7)}{8} - 2$

Multiply $- 1$ by $4$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{p (- 4 + 7)}{8} - 2$

Add $- 4$ and $7$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{p \cdot 3}{8} - 2$

Move $3$ to the left of $p$ .

$\frac{7 p}{8} + \frac{1}{2} = \frac{3 p}{8} - 2$

Move all terms containing $p$ to the left side of the equation.

Subtract $\frac{3 p}{8}$ from both sides of the equation.

$\frac{7 p}{8} + \frac{1}{2} - \frac{3 p}{8} = - 2$

Combine the numerators over the common denominator.

$\frac{7 p - 3 p}{8} + \frac{1}{2} = - 2$

Subtract $3 p$ from $7 p$ .

$\frac{4 p}{8} + \frac{1}{2} = - 2$

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 p$ .

$\frac{4 (p)}{8} + \frac{1}{2} = - 2$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{4 p}{4 \cdot 2} + \frac{1}{2} = - 2$

Cancel the common factor.

$\frac{4 p}{4 \cdot 2} + \frac{1}{2} = - 2$

Rewrite the expression.

$\frac{p}{2} + \frac{1}{2} = - 2$

Move all terms not containing $p$ to the right side of the equation.

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{p}{2} = - 2 - \frac{1}{2}$

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

$\frac{p}{2} = - 2 \cdot \frac{2}{2} - \frac{1}{2}$

Combine $- 2$ and $\frac{2}{2}$ .

$\frac{p}{2} = \frac{- 2 \cdot 2}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{p}{2} = \frac{- 2 \cdot 2 - 1}{2}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$\frac{p}{2} = \frac{- 4 - 1}{2}$

Subtract $1$ from $- 4$ .

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

Move the negative in front of the fraction.

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$p = - 5$

Solve for p -3/8p+1/2+5/4p=-1/2p-2+7/8p

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