Finite Math Examples

$x + 4 y \leq 16$ , $4 x + 5 y \geq 20$

Step 1

Solve $x + 4 y \leq 16$ for $y$ .

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Step 1.1

Subtract $x$ from both sides of the inequality.

$4 y \leq 16 - x$

Step 1.2

Divide each term in $4 y \leq 16 - x$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 y \leq 16 - x$ by $4$ .

$\frac{4 y}{4} \leq \frac{16}{4} + \frac{- x}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} \leq \frac{16}{4} + \frac{- x}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{16}{4} + \frac{- x}{4}$

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 $16$ by $4$ .

$y \leq 4 + \frac{- x}{4}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y \leq 4 - \frac{x}{4}$

Step 2

Solve $4 x + 5 y \geq 20$ for $y$ .

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Step 2.1

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

$5 y \geq 20 - 4 x$

Step 2.2

Divide each term in $5 y \geq 20 - 4 x$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 y \geq 20 - 4 x$ by $5$ .

$\frac{5 y}{5} \geq \frac{20}{5} + \frac{- 4 x}{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} \geq \frac{20}{5} + \frac{- 4 x}{5}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{20}{5} + \frac{- 4 x}{5}$

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 $20$ by $5$ .

$y \geq 4 + \frac{- 4 x}{5}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y \geq 4 - \frac{4 x}{5}$

Step 3

Find the intersection of $y \leq 4 - \frac{x}{4}$ and $y \geq 4 - \frac{4 x}{5}$ .

$4 - \frac{4 x}{5} \leq y \leq 4 - \frac{x}{4}$

Step 4