Solve for n -2(5+6n)<6(8-2n)

$- 2 (5 + 6 n) < 6 (8 - 2 n)$

Step 1

Simplify $- 2 (5 + 6 n)$ .

Rewrite.

$0 + 0 - 2 (5 + 6 n) < 6 (8 - 2 n)$

Simplify by adding zeros.

$- 2 (5 + 6 n) < 6 (8 - 2 n)$

Apply the distributive property.

$- 2 \cdot 5 - 2 (6 n) < 6 (8 - 2 n)$

Multiply.

Multiply $- 2$ by $5$ .

$- 10 - 2 (6 n) < 6 (8 - 2 n)$

Multiply $6$ by $- 2$ .

$- 10 - 12 n < 6 (8 - 2 n)$

Step 2

Simplify $6 (8 - 2 n)$ .

Apply the distributive property.

$- 10 - 12 n < 6 \cdot 8 + 6 (- 2 n)$

Multiply.

Multiply $6$ by $8$ .

$- 10 - 12 n < 48 + 6 (- 2 n)$

Multiply $- 2$ by $6$ .

$- 10 - 12 n < 48 - 12 n$

Step 3

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

Add $12 n$ to both sides of the inequality.

$- 10 - 12 n + 12 n < 48$

Combine the opposite terms in $- 10 - 12 n + 12 n$ .

Add $- 12 n$ and $12 n$ .

$- 10 + 0 < 48$

Add $- 10$ and $0$ .

$- 10 < 48$

Step 4

Since $- 10 < 48$ , the inequality will always be true for any value of $n$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$