Finite Math Examples

$y > 6 - 12 x$

Step 1

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

$6 - 12 x < y$

Step 2

Subtract $6$ from both sides of the inequality.

$- 12 x < y - 6$

Step 3

Divide each term in $- 12 x < y - 6$ by $- 12$ and simplify.

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Step 3.1

Divide each term in $- 12 x < y - 6$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 x}{- 12} > \frac{y}{- 12} + \frac{- 6}{- 12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 12 x}{- 12} > \frac{y}{- 12} + \frac{- 6}{- 12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{y}{- 12} + \frac{- 6}{- 12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Move the negative in front of the fraction.

$x > - \frac{y}{12} + \frac{- 6}{- 12}$

Step 3.3.1.2

Cancel the common factor of $- 6$ and $- 12$ .

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Step 3.3.1.2.1

Factor $- 6$ out of $- 6$ .

$x > - \frac{y}{12} + \frac{- 6 (1)}{- 12}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $- 6$ out of $- 12$ .

$x > - \frac{y}{12} + \frac{- 6 \cdot 1}{- 6 \cdot 2}$

Step 3.3.1.2.2.2

Cancel the common factor.

$x > - \frac{y}{12} + \frac{- 6 \cdot 1}{- 6 \cdot 2}$

Step 3.3.1.2.2.3

Rewrite the expression.

$x > - \frac{y}{12} + \frac{1}{2}$