Solve the Inequality for n 8n+2(-8n+3)<=n+2+9n

$8 n + 2 (- 8 n + 3) \leq n + 2 + 9 n$

Simplify $8 n + 2 (- 8 n + 3)$ .

Simplify each term.

Apply the distributive property.

$8 n + 2 (- 8 n) + 2 \cdot 3 \leq n + 2 + 9 n$

Multiply $- 8$ by $2$ .

$8 n - 16 n + 2 \cdot 3 \leq n + 2 + 9 n$

Multiply $2$ by $3$ .

$8 n - 16 n + 6 \leq n + 2 + 9 n$

Subtract $16 n$ from $8 n$ .

$- 8 n + 6 \leq n + 2 + 9 n$

Add $n$ and $9 n$ .

$- 8 n + 6 \leq 10 n + 2$

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

Subtract $10 n$ from both sides of the inequality.

$- 8 n + 6 - 10 n \leq 2$

Subtract $10 n$ from $- 8 n$ .

$- 18 n + 6 \leq 2$

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

Subtract $6$ from both sides of the inequality.

$- 18 n \leq 2 - 6$

Subtract $6$ from $2$ .

$- 18 n \leq - 4$

Divide each term in $- 18 n \leq - 4$ by $- 18$ and simplify.

Divide each term in $- 18 n \leq - 4$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 n}{- 18} \geq \frac{- 4}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 n}{- 18} \geq \frac{- 4}{- 18}$

Divide $n$ by $1$ .

$n \geq \frac{- 4}{- 18}$

Simplify the right side.

Cancel the common factor of $- 4$ and $- 18$ .

Factor $- 2$ out of $- 4$ .

$n \geq \frac{- 2 (2)}{- 18}$

Cancel the common factors.

Factor $- 2$ out of $- 18$ .

$n \geq \frac{- 2 \cdot 2}{- 2 \cdot 9}$

Cancel the common factor.

$n \geq \frac{- 2 \cdot 2}{- 2 \cdot 9}$

Rewrite the expression.

$n \geq \frac{2}{9}$

The result can be shown in multiple forms.

Inequality Form:

$n \geq \frac{2}{9}$

Interval Notation:

$[\frac{2}{9}, \infty)$

Solve the Inequality for n 8n+2(-8n+3)<=n+2+9n

Related Questions

Support LCMGCF.com by disabling your adblocker.