Solve for n -1/2(2n+4)+6=-9+4(2n+1) ?

$- \frac{1}{2} (2 n + 4) + 6 = - 9 + 4 (2 n + 1)$ ?

Step 1

Simplify $- \frac{1}{2} \cdot (2 n + 4) + 6$ .

Simplify each term.

Apply the distributive property.

$- \frac{1}{2} (2 n) - \frac{1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Cancel the common factor of $2$ .

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

$\frac{- 1}{2} (2 n) - \frac{1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Factor $2$ out of $2 n$ .

$\frac{- 1}{2} (2 (n)) - \frac{1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Cancel the common factor.

$\frac{- 1}{2} (2 n) - \frac{1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Rewrite the expression.

$- 1 n - \frac{1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Cancel the common factor of $2$ .

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

$- 1 n + \frac{- 1}{2} \cdot 4 + 6 = - 9 + 4 (2 n + 1)$

Factor $2$ out of $4$ .

$- 1 n + \frac{- 1}{2} \cdot (2 (2)) + 6 = - 9 + 4 (2 n + 1)$

Cancel the common factor.

$- 1 n + \frac{- 1}{2} \cdot (2 \cdot 2) + 6 = - 9 + 4 (2 n + 1)$

Rewrite the expression.

$- 1 n - 1 \cdot 2 + 6 = - 9 + 4 (2 n + 1)$

Multiply $- 1$ by $2$ .

$- 1 n - 2 + 6 = - 9 + 4 (2 n + 1)$

Rewrite $- 1 n$ as $- n$ .

$- n - 2 + 6 = - 9 + 4 (2 n + 1)$

Add $- 2$ and $6$ .

$- n + 4 = - 9 + 4 (2 n + 1)$

Step 2

Simplify $- 9 + 4 (2 n + 1)$ .

Simplify each term.

Apply the distributive property.

$- n + 4 = - 9 + 4 (2 n) + 4 \cdot 1$

Multiply $2$ by $4$ .

$- n + 4 = - 9 + 8 n + 4 \cdot 1$

Multiply $4$ by $1$ .

$- n + 4 = - 9 + 8 n + 4$

Add $- 9$ and $4$ .

$- n + 4 = 8 n - 5$

Step 3

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

Subtract $8 n$ from both sides of the equation.

$- n + 4 - 8 n = - 5$

Subtract $8 n$ from $- n$ .

$- 9 n + 4 = - 5$

Step 4

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

Subtract $4$ from both sides of the equation.

$- 9 n = - 5 - 4$

Subtract $4$ from $- 5$ .

$- 9 n = - 9$

Step 5

Divide each term in $- 9 n = - 9$ by $- 9$ and simplify.

Divide each term in $- 9 n = - 9$ by $- 9$ .

$\frac{- 9 n}{- 9} = \frac{- 9}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 n}{- 9} = \frac{- 9}{- 9}$

Divide $n$ by $1$ .

$n = \frac{- 9}{- 9}$

Simplify the right side.

Divide $- 9$ by $- 9$ .

$n = 1$

Solve for n -1/2(2n+4)+6=-9+4(2n+1) ?

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