Algebra Examples

$\frac{5}{6} v < \frac{8}{5}$

Step 1

Multiply each term in $\frac{5}{6} v < \frac{8}{5}$ by $\frac{6}{5}$ .

$\frac{5}{6} v \frac{6}{5} < \frac{8}{5} \cdot \frac{6}{5}$

Step 2

Simplify the left side.

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Combine $\frac{5}{6}$ and $v$ .

$\frac{5 v}{6} \cdot \frac{6}{5} < \frac{8}{5} \cdot \frac{6}{5}$

Cancel the common factor of $5$ .

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Factor $5$ out of $5 v$ .

$\frac{5 (v)}{6} \cdot \frac{6}{5} < \frac{8}{5} \cdot \frac{6}{5}$

Cancel the common factor.

$\frac{5 v}{6} \cdot \frac{6}{5} < \frac{8}{5} \cdot \frac{6}{5}$

Rewrite the expression.

$\frac{v}{6} \cdot 6 < \frac{8}{5} \cdot \frac{6}{5}$

Cancel the common factor of $6$ .

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Cancel the common factor.

$\frac{v}{6} \cdot 6 < \frac{8}{5} \cdot \frac{6}{5}$

Rewrite the expression.

$v < \frac{8}{5} \cdot \frac{6}{5}$

Step 3

Simplify the right side.

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Multiply $\frac{8}{5} \cdot \frac{6}{5}$ .

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Multiply $\frac{8}{5}$ by $\frac{6}{5}$ .

$v < \frac{8 \cdot 6}{5 \cdot 5}$

Multiply $8$ by $6$ .

$v < \frac{48}{5 \cdot 5}$

Multiply $5$ by $5$ .

$v < \frac{48}{25}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$v < \frac{48}{25}$

Interval Notation:

$(- \infty, \frac{48}{25})$