Finite Math Examples

$- 5 < 3 x < \frac{4}{3}$

Step 1

Divide each term in the inequality by $3$ .

$\frac{- 5}{3} < \frac{3 x}{3} < \frac{\frac{4}{3}}{3}$

Step 2

Move the negative in front of the fraction.

$- \frac{5}{3} < \frac{3 x}{3} < \frac{\frac{4}{3}}{3}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$- \frac{5}{3} < \frac{3 x}{3} < \frac{\frac{4}{3}}{3}$

Step 3.2

Divide $x$ by $1$ .

$- \frac{5}{3} < x < \frac{\frac{4}{3}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{5}{3} < x < \frac{4}{3} \cdot \frac{1}{3}$

Step 5

Multiply $\frac{4}{3} \cdot \frac{1}{3}$ .

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Step 5.1

Multiply $\frac{4}{3}$ by $\frac{1}{3}$ .

$- \frac{5}{3} < x < \frac{4}{3 \cdot 3}$

Step 5.2

Multiply $3$ by $3$ .

$- \frac{5}{3} < x < \frac{4}{9}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{3} < x < \frac{4}{9}$

Interval Notation:

$(- \frac{5}{3}, \frac{4}{9})$

Step 7