Solve the Inequality for n -5n-6n<=8-8n-n

$- 5 n - 6 n \leq 8 - 8 n - n$

Step 1

Subtract $6 n$ from $- 5 n$ .

$- 11 n \leq 8 - 8 n - n$

Step 2

Subtract $n$ from $- 8 n$ .

$- 11 n \leq 8 - 9 n$

Step 3

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

Add $9 n$ to both sides of the inequality.

$- 11 n + 9 n \leq 8$

Add $- 11 n$ and $9 n$ .

$- 2 n \leq 8$

Step 4

Divide each term in $- 2 n \leq 8$ by $- 2$ and simplify.

Divide each term in $- 2 n \leq 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 n}{- 2} \geq \frac{8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 n}{- 2} \geq \frac{8}{- 2}$

Divide $n$ by $1$ .

$n \geq \frac{8}{- 2}$

Simplify the right side.

Divide $8$ by $- 2$ .

$n \geq - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$n \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve the Inequality for n -5n-6n<=8-8n-n

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