Solve the Inequality for n |n|-3>-2

$| n | - 3 > - 2$

Write $| n | - 3 > - 2$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$n \geq 0$

In the piece where $n$ is non-negative, remove the absolute value.

$n - 3 > - 2$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$n < 0$

In the piece where $n$ is negative, remove the absolute value and multiply by $- 1$ .

$- n - 3 > - 2$

Write as a piecewise.

${\begin{cases} n - 3 > - 2 & n \geq 0 \\ - n - 3 > - 2 & n < 0 \end{cases}$

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

Add $3$ to both sides of the inequality.

$n > - 2 + 3$

Add $- 2$ and $3$ .

$n > 1$

Solve $- n - 3 > - 2$ for $n$ .

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

Add $3$ to both sides of the inequality.

$- n > - 2 + 3$

Add $- 2$ and $3$ .

$- n > 1$

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

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.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $n$ by $1$ .

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

Simplify the right side.

Divide $1$ by $- 1$ .

$n < - 1$

Find the union of the solutions.

$n < - 1$ or $n > 1$

The result can be shown in multiple forms.

Inequality Form:

$n < - 1 or n > 1$

Interval Notation:

$(- \infty, - 1) \cup (1, \infty)$

Solve the Inequality for n |n|-3>-2

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