Solve the Inequality for n 6n-(n+1)<3n-2+5n

$6 n - (n + 1) < 3 n - 2 + 5 n$

Step 1

Simplify $6 n - (n + 1)$ .

Simplify each term.

Apply the distributive property.

$6 n - n - 1 \cdot 1 < 3 n - 2 + 5 n$

Multiply $- 1$ by $1$ .

$6 n - n - 1 < 3 n - 2 + 5 n$

Subtract $n$ from $6 n$ .

$5 n - 1 < 3 n - 2 + 5 n$

Step 2

Add $3 n$ and $5 n$ .

$5 n - 1 < 8 n - 2$

Step 3

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

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

$5 n - 1 - 8 n < - 2$

Subtract $8 n$ from $5 n$ .

$- 3 n - 1 < - 2$

Step 4

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

Add $1$ to both sides of the inequality.

$- 3 n < - 2 + 1$

Add $- 2$ and $1$ .

$- 3 n < - 1$

Step 5

Divide each term in $- 3 n < - 1$ by $- 3$ and simplify.

Divide each term in $- 3 n < - 1$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 n}{- 3} > \frac{- 1}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 n}{- 3} > \frac{- 1}{- 3}$

Divide $n$ by $1$ .

$n > \frac{- 1}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$n > \frac{1}{3}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$n > \frac{1}{3}$

Interval Notation:

$(\frac{1}{3}, \infty)$

Solve the Inequality for n 6n-(n+1)<3n-2+5n

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