Solve the Inequality for n -4n-5(10n+5)<-8n-1-6n

$- 4 n - 5 (10 n + 5) < - 8 n - 1 - 6 n$

Step 1

Simplify $- 4 n - 5 (10 n + 5)$ .

Simplify each term.

Apply the distributive property.

$- 4 n - 5 (10 n) - 5 \cdot 5 < - 8 n - 1 - 6 n$

Multiply $10$ by $- 5$ .

$- 4 n - 50 n - 5 \cdot 5 < - 8 n - 1 - 6 n$

Multiply $- 5$ by $5$ .

$- 4 n - 50 n - 25 < - 8 n - 1 - 6 n$

Subtract $50 n$ from $- 4 n$ .

$- 54 n - 25 < - 8 n - 1 - 6 n$

Step 2

Subtract $6 n$ from $- 8 n$ .

$- 54 n - 25 < - 14 n - 1$

Step 3

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

Add $14 n$ to both sides of the inequality.

$- 54 n - 25 + 14 n < - 1$

Add $- 54 n$ and $14 n$ .

$- 40 n - 25 < - 1$

Step 4

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

Add $25$ to both sides of the inequality.

$- 40 n < - 1 + 25$

Add $- 1$ and $25$ .

$- 40 n < 24$

Step 5

Divide each term in $- 40 n < 24$ by $- 40$ and simplify.

Divide each term in $- 40 n < 24$ by $- 40$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 40 n}{- 40} > \frac{24}{- 40}$

Simplify the left side.

Cancel the common factor of $- 40$ .

Cancel the common factor.

$\frac{- 40 n}{- 40} > \frac{24}{- 40}$

Divide $n$ by $1$ .

$n > \frac{24}{- 40}$

Simplify the right side.

Cancel the common factor of $24$ and $- 40$ .

Factor $8$ out of $24$ .

$n > \frac{8 (3)}{- 40}$

Cancel the common factors.

Factor $8$ out of $- 40$ .

$n > \frac{8 \cdot 3}{8 \cdot - 5}$

Cancel the common factor.

$n > \frac{8 \cdot 3}{8 \cdot - 5}$

Rewrite the expression.

$n > \frac{3}{- 5}$

Move the negative in front of the fraction.

$n > - \frac{3}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$n > - \frac{3}{5}$

Interval Notation:

$(- \frac{3}{5}, \infty)$

Solve the Inequality for n -4n-5(10n+5)<-8n-1-6n

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