Solve the Inequality for n 5n-3(n-6)>=0

$5 n - 3 (n - 6) \geq 0$

Step 1

Simplify $5 n - 3 (n - 6)$ .

Simplify each term.

Apply the distributive property.

$5 n - 3 n - 3 \cdot - 6 \geq 0$

Multiply $- 3$ by $- 6$ .

$5 n - 3 n + 18 \geq 0$

Subtract $3 n$ from $5 n$ .

$2 n + 18 \geq 0$

Step 2

Subtract $18$ from both sides of the inequality.

$2 n \geq - 18$

Step 3

Divide each term in $2 n \geq - 18$ by $2$ and simplify.

Divide each term in $2 n \geq - 18$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Divide $- 18$ by $2$ .

$n \geq - 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n \geq - 9$

Interval Notation:

$[- 9, \infty)$