Algebra Examples

$- 2 > \frac{v}{- 3}$

Step 1

Multiply both sides by $- 3$ .

$- 2 \cdot - 3 < \frac{v}{- 3} \cdot - 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Multiply $- 2$ by $- 3$ .

$6 < \frac{v}{- 3} \cdot - 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{v}{- 3} \cdot - 3$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $- 3$ .

$6 < \frac{v}{3 (- 1)} \cdot - 3$

Step 2.2.1.1.2

Factor $3$ out of $- 3$ .

$6 < \frac{v}{3 \cdot - 1} \cdot (3 \cdot - 1)$

Step 2.2.1.1.3

Cancel the common factor.

$6 < \frac{v}{3 \cdot - 1} \cdot (3 \cdot - 1)$

Step 2.2.1.1.4

Rewrite the expression.

$6 < \frac{v}{- 1} \cdot - 1$

Step 2.2.1.2

Combine $\frac{v}{- 1}$ and $- 1$ .

$6 < \frac{v \cdot - 1}{- 1}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Move the negative one from the denominator of $\frac{v \cdot - 1}{- 1}$ .

$6 < - 1 \cdot (v \cdot - 1)$

Step 2.2.1.3.2

Rewrite $- 1 \cdot (v \cdot - 1)$ as $- (v \cdot - 1)$ .

$6 < - (v \cdot - 1)$

Step 2.2.1.3.3

Move $- 1$ to the left of $v$ .

$6 < - (- 1 \cdot v)$

Step 2.2.1.3.4

Rewrite $- 1 v$ as $- v$ .

$6 < - - v$

Step 2.2.1.4

Multiply $- - v$ .

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Step 2.2.1.4.1

Multiply $- 1$ by $- 1$ .

$6 < 1 v$

Step 2.2.1.4.2

Multiply $v$ by $1$ .

$6 < v$

Step 3

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

$v > 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$v > 6$

Interval Notation:

$(6, \infty)$