Finite Math Examples

$x - 5 y < 10$ , $x - y > - 2$

Step 1

Solve $x - 5 y < 10$ for $y$ .

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Step 1.1

Subtract $x$ from both sides of the inequality.

$- 5 y < 10 - x$

Step 1.2

Divide each term in $- 5 y < 10 - x$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 y < 10 - x$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 y}{- 5} > \frac{10}{- 5} + \frac{- x}{- 5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} > \frac{10}{- 5} + \frac{- x}{- 5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{10}{- 5} + \frac{- x}{- 5}$

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 $10$ by $- 5$ .

$y > - 2 + \frac{- x}{- 5}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y > - 2 + \frac{x}{5}$

Step 2

Solve $x - y > - 2$ for $y$ .

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Step 2.1

Subtract $x$ from both sides of the inequality.

$- y > - 2 - x$

Step 2.2

Divide each term in $- y > - 2 - x$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- y > - 2 - x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{- 2}{- 1} + \frac{- x}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{- 2}{- 1} + \frac{- x}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y < \frac{- 2}{- 1} + \frac{- x}{- 1}$

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 $- 2$ by $- 1$ .

$y < 2 + \frac{- x}{- 1}$

Step 2.2.3.1.2

Dividing two negative values results in a positive value.

$y < 2 + \frac{x}{1}$

Step 2.2.3.1.3

Divide $x$ by $1$ .

$y < 2 + x$

Step 3

Find the intersection of $y > - 2 + \frac{x}{5}$ and $y < 2 + x$ .

$- 2 + \frac{x}{5} < y < 2 + x$

Step 4