Finite Math Examples

$3 x - 9 y > 12$

Step 1

Subtract $3 x$ from both sides of the inequality.

$- 9 y > 12 - 3 x$

Step 2

Divide each term in $- 9 y > 12 - 3 x$ by $- 9$ and simplify.

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Step 2.1

Divide each term in $- 9 y > 12 - 3 x$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 y}{- 9} < \frac{12}{- 9} + \frac{- 3 x}{- 9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 9 y}{- 9} < \frac{12}{- 9} + \frac{- 3 x}{- 9}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y < \frac{12}{- 9} + \frac{- 3 x}{- 9}$

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

Cancel the common factor of $12$ and $- 9$ .

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Step 2.3.1.1.1

Factor $3$ out of $12$ .

$y < \frac{3 (4)}{- 9} + \frac{- 3 x}{- 9}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $3$ out of $- 9$ .

$y < \frac{3 \cdot 4}{3 \cdot - 3} + \frac{- 3 x}{- 9}$

Step 2.3.1.1.2.2

Cancel the common factor.

$y < \frac{3 \cdot 4}{3 \cdot - 3} + \frac{- 3 x}{- 9}$

Step 2.3.1.1.2.3

Rewrite the expression.

$y < \frac{4}{- 3} + \frac{- 3 x}{- 9}$

Step 2.3.1.2

Move the negative in front of the fraction.

$y < - \frac{4}{3} + \frac{- 3 x}{- 9}$

Step 2.3.1.3

Cancel the common factor of $- 3$ and $- 9$ .

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Step 2.3.1.3.1

Factor $- 3$ out of $- 3 x$ .

$y < - \frac{4}{3} + \frac{- 3 (x)}{- 9}$

Step 2.3.1.3.2

Cancel the common factors.

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Step 2.3.1.3.2.1

Factor $- 3$ out of $- 9$ .

$y < - \frac{4}{3} + \frac{- 3 (x)}{- 3 (3)}$

Step 2.3.1.3.2.2

Cancel the common factor.

$y < - \frac{4}{3} + \frac{- 3 x}{- 3 \cdot 3}$

Step 2.3.1.3.2.3

Rewrite the expression.

$y < - \frac{4}{3} + \frac{x}{3}$