Solve for p -1/2(6p+16)=7

$- \frac{1}{2} (6 p + 16) = 7$

Step 1

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cdot (6 p + 16)) = - 2 \cdot 7$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{1}{2} \cdot (6 p + 16))$ .

Apply the distributive property.

$- 2 (- \frac{1}{2} (6 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 (\frac{- 1}{2} (6 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Factor $2$ out of $6 p$ .

$- 2 (\frac{- 1}{2} (2 (3 p)) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Cancel the common factor.

$- 2 (\frac{- 1}{2} (2 (3 p)) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Rewrite the expression.

$- 2 (- 1 (3 p) - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Multiply $3$ by $- 1$ .

$- 2 (- 3 p - \frac{1}{2} \cdot 16) = - 2 \cdot 7$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 2 (- 3 p + \frac{- 1}{2} \cdot 16) = - 2 \cdot 7$

Factor $2$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 (- 3 p - 1 \cdot 8) = - 2 \cdot 7$

Multiply $- 1$ by $8$ .

$- 2 (- 3 p - 8) = - 2 \cdot 7$

Apply the distributive property.

$- 2 (- 3 p) - 2 \cdot - 8 = - 2 \cdot 7$

Multiply.

Multiply $- 3$ by $- 2$ .

$6 p - 2 \cdot - 8 = - 2 \cdot 7$

Multiply $- 2$ by $- 8$ .

$6 p + 16 = - 2 \cdot 7$

Simplify the right side.

Multiply $- 2$ by $7$ .

$6 p + 16 = - 14$

Step 3

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

Subtract $16$ from both sides of the equation.

$6 p = - 14 - 16$

Subtract $16$ from $- 14$ .

$6 p = - 30$

Step 4

Divide each term in $6 p = - 30$ by $6$ and simplify.

Divide each term in $6 p = - 30$ by $6$ .

$\frac{6 p}{6} = \frac{- 30}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 p}{6} = \frac{- 30}{6}$

Divide $p$ by $1$ .

$p = \frac{- 30}{6}$

Simplify the right side.

Divide $- 30$ by $6$ .

$p = - 5$

Solve for p -1/2(6p+16)=7

Related Questions

Support LCMGCF.com by disabling your adblocker.