Finite Math Examples

$n + 6 > 2 n + 5 > n - 2$

Step 1

Solve $n + 6 > 2 n + 5$ for $n$ .

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Step 1.1

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

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Step 1.1.1

Subtract $2 n$ from both sides of the inequality.

$n + 6 - 2 n > 5$

Step 1.1.2

Subtract $2 n$ from $n$ .

$- n + 6 > 5$

Step 1.2

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

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Step 1.2.1

Subtract $6$ from both sides of the inequality.

$- n > 5 - 6$

Step 1.2.2

Subtract $6$ from $5$ .

$- n > - 1$

Step 1.3

Divide each term in $- n > - 1$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- n > - 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- n}{- 1} < \frac{- 1}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} < \frac{- 1}{- 1}$

Step 1.3.2.2

Divide $n$ by $1$ .

$n < \frac{- 1}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $- 1$ by $- 1$ .

$n < 1$

Step 2

Solve $2 n + 5 > n - 2$ for $n$ .

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Step 2.1

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

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Step 2.1.1

Subtract $n$ from both sides of the inequality.

$2 n + 5 - n > - 2$

Step 2.1.2

Subtract $n$ from $2 n$ .

$n + 5 > - 2$

Step 2.2

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

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Step 2.2.1

Subtract $5$ from both sides of the inequality.

$n > - 2 - 5$

Step 2.2.2

Subtract $5$ from $- 2$ .

$n > - 7$

Step 3

Find the intersection of $n < 1$ and $n > - 7$ .

$- 7 < n < 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 7 < n < 1$

Interval Notation:

$(- 7, 1)$

Step 5