Finite Math Examples

$6 x + 2 y > 12$ , $4 x - 3 y < 12$

Step 1

Solve $6 x + 2 y > 12$ for $y$ .

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Step 1.1

Subtract $6 x$ from both sides of the inequality.

$2 y > 12 - 6 x$

Step 1.2

Divide each term in $2 y > 12 - 6 x$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y > 12 - 6 x$ by $2$ .

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $12$ by $2$ .

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

Step 1.2.3.1.2

Cancel the common factor of $- 6$ and $2$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 6 x$ .

$y > 6 + \frac{2 (- 3 x)}{2}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $2$ .

$y > 6 + \frac{2 (- 3 x)}{2 (1)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y > 6 + \frac{2 (- 3 x)}{2 \cdot 1}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y > 6 + \frac{- 3 x}{1}$

Step 1.2.3.1.2.2.4

Divide $- 3 x$ by $1$ .

$y > 6 - 3 x$

Step 2

Solve $4 x - 3 y < 12$ for $y$ .

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Step 2.1

Subtract $4 x$ from both sides of the inequality.

$- 3 y < 12 - 4 x$

Step 2.2

Divide each term in $- 3 y < 12 - 4 x$ by $- 3$ and simplify.

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Step 2.2.1

Divide each term in $- 3 y < 12 - 4 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{12}{- 3} + \frac{- 4 x}{- 3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $12$ by $- 3$ .

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

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 3

Find the intersection of $y > 6 - 3 x$ and $y > - 4 + \frac{4 x}{3}$ .

$y > 6 - 3 x$ and $y > - 4 + \frac{4 x}{3}$

Step 4