Solve for n 8-5n<3n-4(n-9)

$8 - 5 n < 3 n - 4 (n - 9)$

Step 1

Rewrite so $n$ is on the left side of the inequality.

$3 n - 4 (n - 9) > 8 - 5 n$

Step 2

Simplify $3 n - 4 (n - 9)$ .

Simplify each term.

Apply the distributive property.

$3 n - 4 n - 4 \cdot - 9 > 8 - 5 n$

Multiply $- 4$ by $- 9$ .

$3 n - 4 n + 36 > 8 - 5 n$

Subtract $4 n$ from $3 n$ .

$- n + 36 > 8 - 5 n$

Step 3

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

Add $5 n$ to both sides of the inequality.

$- n + 36 + 5 n > 8$

Add $- n$ and $5 n$ .

$4 n + 36 > 8$

Step 4

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

Subtract $36$ from both sides of the inequality.

$4 n > 8 - 36$

Subtract $36$ from $8$ .

$4 n > - 28$

Step 5

Divide each term in $4 n > - 28$ by $4$ and simplify.

Divide each term in $4 n > - 28$ by $4$ .

$\frac{4 n}{4} > \frac{- 28}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 n}{4} > \frac{- 28}{4}$

Divide $n$ by $1$ .

$n > \frac{- 28}{4}$

Simplify the right side.

Divide $- 28$ by $4$ .

$n > - 7$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$n > - 7$

Interval Notation:

$(- 7, \infty)$