Solve the Inequality for n 2(n+14)>-1/2(70+2n)

$2 (n + 14) > - \frac{1}{2} (70 + 2 n)$

Simplify $2 (n + 14)$ .

Start simplifying.

$0 + 0 + 2 (n + 14) > - \frac{1}{2} \cdot (70 + 2 n)$

Simplify by adding zeros.

$2 (n + 14) > - \frac{1}{2} \cdot (70 + 2 n)$

Apply the distributive property.

$2 n + 2 \cdot 14 > - \frac{1}{2} \cdot (70 + 2 n)$

Multiply $2$ by $14$ .

$2 n + 28 > - \frac{1}{2} \cdot (70 + 2 n)$

Simplify $- \frac{1}{2} \cdot (70 + 2 n)$ .

Apply the distributive property.

$2 n + 28 > - \frac{1}{2} \cdot 70 - \frac{1}{2} (2 n)$

Cancel the common factor of $2$ .

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

$2 n + 28 > \frac{- 1}{2} \cdot 70 - \frac{1}{2} (2 n)$

Factor $2$ out of $70$ .

$2 n + 28 > \frac{- 1}{2} \cdot (2 (35)) - \frac{1}{2} (2 n)$

Cancel the common factor.

$2 n + 28 > \frac{- 1}{2} \cdot (2 \cdot 35) - \frac{1}{2} (2 n)$

Rewrite the expression.

$2 n + 28 > - 1 \cdot 35 - \frac{1}{2} (2 n)$

Multiply $- 1$ by $35$ .

$2 n + 28 > - 35 - \frac{1}{2} (2 n)$

Cancel the common factor of $2$ .

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

$2 n + 28 > - 35 + \frac{- 1}{2} (2 n)$

Factor $2$ out of $2 n$ .

$2 n + 28 > - 35 + \frac{- 1}{2} (2 (n))$

Cancel the common factor.

$2 n + 28 > - 35 + \frac{- 1}{2} (2 n)$

Rewrite the expression.

$2 n + 28 > - 35 - 1 n$

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

$2 n + 28 > - 35 - n$

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

Add $n$ to both sides of the inequality.

$2 n + 28 + n > - 35$

Add $2 n$ and $n$ .

$3 n + 28 > - 35$

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

Subtract $28$ from both sides of the inequality.

$3 n > - 35 - 28$

Subtract $28$ from $- 35$ .

$3 n > - 63$

Divide each term in $3 n > - 63$ by $3$ and simplify.

Divide each term in $3 n > - 63$ by $3$ .

$\frac{3 n}{3} > \frac{- 63}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} > \frac{- 63}{3}$

Divide $n$ by $1$ .

$n > \frac{- 63}{3}$

Simplify the right side.

Divide $- 63$ by $3$ .

$n > - 21$

The result can be shown in multiple forms.

Inequality Form:

$n > - 21$

Interval Notation:

$(- 21, \infty)$

Solve the Inequality for n 2(n+14)>-1/2(70+2n)

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