Solve the Inequality for n n-5<=5n-1

$n - 5 \leq 5 n - 1$

Step 1

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

Subtract $5 n$ from both sides of the inequality.

$n - 5 - 5 n \leq - 1$

Subtract $5 n$ from $n$ .

$- 4 n - 5 \leq - 1$

Step 2

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

Add $5$ to both sides of the inequality.

$- 4 n \leq - 1 + 5$

Add $- 1$ and $5$ .

$- 4 n \leq 4$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Divide $4$ by $- 4$ .

$n \geq - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n \geq - 1$

Interval Notation:

$[- 1, \infty)$

Solve the Inequality for n n-5<=5n-1

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