Solve the Inequality for n 9n+3(2n+8)<-10n-4-8

$9 n + 3 (2 n + 8) < - 10 n - 4 - 8$

Step 1

Simplify $9 n + 3 (2 n + 8)$ .

Simplify each term.

Apply the distributive property.

$9 n + 3 (2 n) + 3 \cdot 8 < - 10 n - 4 - 8$

Multiply $2$ by $3$ .

$9 n + 6 n + 3 \cdot 8 < - 10 n - 4 - 8$

Multiply $3$ by $8$ .

$9 n + 6 n + 24 < - 10 n - 4 - 8$

Add $9 n$ and $6 n$ .

$15 n + 24 < - 10 n - 4 - 8$

Step 2

Subtract $8$ from $- 4$ .

$15 n + 24 < - 10 n - 12$

Step 3

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

Add $10 n$ to both sides of the inequality.

$15 n + 24 + 10 n < - 12$

Add $15 n$ and $10 n$ .

$25 n + 24 < - 12$

Step 4

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

Subtract $24$ from both sides of the inequality.

$25 n < - 12 - 24$

Subtract $24$ from $- 12$ .

$25 n < - 36$

Step 5

Divide each term in $25 n < - 36$ by $25$ and simplify.

Divide each term in $25 n < - 36$ by $25$ .

$\frac{25 n}{25} < \frac{- 36}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 n}{25} < \frac{- 36}{25}$

Divide $n$ by $1$ .

$n < \frac{- 36}{25}$

Simplify the right side.

Move the negative in front of the fraction.

$n < - \frac{36}{25}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$n < - \frac{36}{25}$

Interval Notation:

$(- \infty, - \frac{36}{25})$

Solve the Inequality for n 9n+3(2n+8)<-10n-4-8

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