Solve for p 9-4(2p-1)=41

$9 - 4 (2 p - 1) = 41$

Simplify $9 - 4 (2 p - 1)$ .

Simplify each term.

Apply the distributive property.

$9 - 4 (2 p) - 4 \cdot - 1 = 41$

Multiply $2$ by $- 4$ .

$9 - 8 p - 4 \cdot - 1 = 41$

Multiply $- 4$ by $- 1$ .

$9 - 8 p + 4 = 41$

Add $9$ and $4$ .

$- 8 p + 13 = 41$

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

Subtract $13$ from both sides of the equation.

$- 8 p = 41 - 13$

Subtract $13$ from $41$ .

$- 8 p = 28$

Divide each term in $- 8 p = 28$ by $- 8$ and simplify.

Divide each term in $- 8 p = 28$ by $- 8$ .

$\frac{- 8 p}{- 8} = \frac{28}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 p}{- 8} = \frac{28}{- 8}$

Divide $p$ by $1$ .

$p = \frac{28}{- 8}$

Simplify the right side.

Cancel the common factor of $28$ and $- 8$ .

Factor $4$ out of $28$ .

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

Cancel the common factors.

Factor $4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

$p = \frac{7}{- 2}$

Move the negative in front of the fraction.

$p = - \frac{7}{2}$

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{7}{2}$

Decimal Form:

$p = - 3.5$

Mixed Number Form:

$p = - 3 \frac{1}{2}$