Algebra Examples

$- 4 p < \frac{2}{3}$

Step 1

Divide each term in $- 4 p < \frac{2}{3}$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 p}{- 4} > \frac{\frac{2}{3}}{- 4}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $- 4$ .

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Step 2.1.1

Cancel the common factor.

$\frac{- 4 p}{- 4} > \frac{\frac{2}{3}}{- 4}$

Step 2.1.2

Divide $p$ by $1$ .

$p > \frac{\frac{2}{3}}{- 4}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$p > \frac{2}{3} \cdot \frac{1}{- 4}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $- 4$ .

$p > \frac{2}{3} \cdot \frac{1}{2 (- 2)}$

Step 3.2.2

Cancel the common factor.

$p > \frac{2}{3} \cdot \frac{1}{2 \cdot - 2}$

Step 3.2.3

Rewrite the expression.

$p > \frac{1}{3} \cdot \frac{1}{- 2}$

Step 3.3

Multiply $\frac{1}{3}$ by $\frac{1}{- 2}$ .

$p > \frac{1}{3 \cdot - 2}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Multiply $3$ by $- 2$ .

$p > \frac{1}{- 6}$

Step 3.4.2

Move the negative in front of the fraction.

$p > - \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$p > - \frac{1}{6}$

Interval Notation:

$(- \frac{1}{6}, \infty)$