Solve the Inequality for n 10+3(-9n+1)>-2n-2+4

$10 + 3 (- 9 n + 1) > - 2 n - 2 + 4$

Step 1

Simplify $10 + 3 (- 9 n + 1)$ .

Simplify each term.

Apply the distributive property.

$10 + 3 (- 9 n) + 3 \cdot 1 > - 2 n - 2 + 4$

Multiply $- 9$ by $3$ .

$10 - 27 n + 3 \cdot 1 > - 2 n - 2 + 4$

Multiply $3$ by $1$ .

$10 - 27 n + 3 > - 2 n - 2 + 4$

Add $10$ and $3$ .

$- 27 n + 13 > - 2 n - 2 + 4$

Step 2

Add $- 2$ and $4$ .

$- 27 n + 13 > - 2 n + 2$

Step 3

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

Add $2 n$ to both sides of the inequality.

$- 27 n + 13 + 2 n > 2$

Add $- 27 n$ and $2 n$ .

$- 25 n + 13 > 2$

Step 4

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

Subtract $13$ from both sides of the inequality.

$- 25 n > 2 - 13$

Subtract $13$ from $2$ .

$- 25 n > - 11$

Step 5

Divide each term in $- 25 n > - 11$ by $- 25$ and simplify.

Divide each term in $- 25 n > - 11$ by $- 25$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 25 n}{- 25} < \frac{- 11}{- 25}$

Simplify the left side.

Cancel the common factor of $- 25$ .

Cancel the common factor.

$\frac{- 25 n}{- 25} < \frac{- 11}{- 25}$

Divide $n$ by $1$ .

$n < \frac{- 11}{- 25}$

Simplify the right side.

Dividing two negative values results in a positive value.

$n < \frac{11}{25}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$n < \frac{11}{25}$

Interval Notation:

$(- \infty, \frac{11}{25})$

Solve the Inequality for n 10+3(-9n+1)>-2n-2+4

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