Finite Math Examples

$x + y \geq - 1$ , $3 x - y \leq 5$

Step 1

Subtract $x$ from both sides of the inequality.

$y \geq - 1 - x$

Step 2

Solve $3 x - y \leq 5$ for $y$ .

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Step 2.1

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

$- y \leq 5 - 3 x$

Step 2.2

Divide each term in $- y \leq 5 - 3 x$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- y \leq 5 - 3 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} \geq \frac{5}{- 1} + \frac{- 3 x}{- 1}$

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.

$\frac{y}{1} \geq \frac{5}{- 1} + \frac{- 3 x}{- 1}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y \geq \frac{5}{- 1} + \frac{- 3 x}{- 1}$

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 $5$ by $- 1$ .

$y \geq - 5 + \frac{- 3 x}{- 1}$

Step 2.2.3.1.2

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y \geq - 5 - 1 \cdot (- 3 x)$

Step 2.2.3.1.3

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y \geq - 5 - (- 3 x)$

Step 2.2.3.1.4

Multiply $- 3$ by $- 1$ .

$y \geq - 5 + 3 x$

Step 3

Find the intersection of $y \geq - 1 - x$ and $y \geq - 5 + 3 x$ .

$y \geq - 1 - x$ and $y \geq - 5 + 3 x$

Step 4