Pre-Algebra Examples

$\frac{6}{10} > n$ , $n > \frac{1}{3}$

Step 1

Solve $\frac{6}{10} > n$ for $n$ .

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Step 1.1

Rewrite so $n$ is on the left side of the inequality.

$n < \frac{6}{10}$

Step 1.2

Cancel the common factor of $6$ and $10$ .

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Step 1.2.1

Factor $2$ out of $6$ .

$n < \frac{2 (3)}{10}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $10$ .

$n < \frac{2 \cdot 3}{2 \cdot 5}$

Step 1.2.2.2

Cancel the common factor.

$n < \frac{2 \cdot 3}{2 \cdot 5}$

Step 1.2.2.3

Rewrite the expression.

$n < \frac{3}{5}$

Step 2

Find the intersection of $n < \frac{3}{5}$ and $n > \frac{1}{3}$ .

$\frac{1}{3} < n < \frac{3}{5}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{3} < n < \frac{3}{5}$

Interval Notation:

$(\frac{1}{3}, \frac{3}{5})$

Step 4