Solve for n 3(n+6)>=3n+8

$3 (n + 6) \geq 3 n + 8$

Simplify $3 (n + 6)$ .

Rewrite.

$0 + 0 + 3 (n + 6) \geq 3 n + 8$

Simplify by adding zeros.

$3 (n + 6) \geq 3 n + 8$

Apply the distributive property.

$3 n + 3 \cdot 6 \geq 3 n + 8$

Multiply $3$ by $6$ .

$3 n + 18 \geq 3 n + 8$

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

Subtract $3 n$ from both sides of the inequality.

$3 n + 18 - 3 n \geq 8$

Combine the opposite terms in $3 n + 18 - 3 n$ .

Subtract $3 n$ from $3 n$ .

$0 + 18 \geq 8$

Add $0$ and $18$ .

$18 \geq 8$

Since $18 \geq 8$ , the inequality will always be true for any value of $n$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$