Finite Math Examples

$5 x - \frac{1}{3 y} < 6$

Step 1

Add $\frac{1}{3 y}$ to both sides of the inequality.

$5 x < 6 + \frac{1}{3 y}$

Step 2

Divide each term in $5 x < 6 + \frac{1}{3 y}$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x < 6 + \frac{1}{3 y}$ by $5$ .

$\frac{5 x}{5} < \frac{6}{5} + \frac{\frac{1}{3 y}}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} < \frac{6}{5} + \frac{\frac{1}{3 y}}{5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{5} + \frac{\frac{1}{3 y}}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x < \frac{6}{5} + \frac{1}{3 y} \cdot \frac{1}{5}$

Step 2.3.1.2

Multiply $\frac{1}{3 y} \cdot \frac{1}{5}$ .

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Step 2.3.1.2.1

Multiply $\frac{1}{3 y}$ by $\frac{1}{5}$ .

$x < \frac{6}{5} + \frac{1}{3 y \cdot 5}$

Step 2.3.1.2.2

Multiply $5$ by $3$ .

$x < \frac{6}{5} + \frac{1}{15 y}$