Solve for p 5p=4(1/2p-1)

$5 p = 4 (\frac{1}{2} p - 1)$

Step 1

Simplify $4 (\frac{1}{2} p - 1)$ .

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

$5 p = 4 (\frac{p}{2} - 1)$

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$5 p = 2 (2) \frac{p}{2} + 4 \cdot - 1$

Cancel the common factor.

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

Rewrite the expression.

$5 p = 2 p + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$5 p = 2 p - 4$

Step 2

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

Subtract $2 p$ from both sides of the equation.

$5 p - 2 p = - 4$

Subtract $2 p$ from $5 p$ .

$3 p = - 4$

Step 3

Divide each term in $3 p = - 4$ by $3$ and simplify.

Divide each term in $3 p = - 4$ by $3$ .

$\frac{3 p}{3} = \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 p}{3} = \frac{- 4}{3}$

Divide $p$ by $1$ .

$p = \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$p = - \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{4}{3}$

Decimal Form:

$p = - 1.\overline{3}$

Mixed Number Form:

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