Finite Math Examples

$2 x + y \leq 30$ , $x + 2 y \leq 24$

Step 1

Subtract $2 x$ from both sides of the inequality.

$y \leq 30 - 2 x$

Step 2

Solve $x + 2 y \leq 24$ for $y$ .

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Step 2.1

Subtract $x$ from both sides of the inequality.

$2 y \leq 24 - x$

Step 2.2

Divide each term in $2 y \leq 24 - x$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 y \leq 24 - x$ by $2$ .

$\frac{2 y}{2} \leq \frac{24}{2} + \frac{- x}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} \leq \frac{24}{2} + \frac{- x}{2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{24}{2} + \frac{- x}{2}$

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 $24$ by $2$ .

$y \leq 12 + \frac{- x}{2}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y \leq 12 - \frac{x}{2}$

Step 3

Find the intersection of $y \leq 30 - 2 x$ and $y \leq 12 - \frac{x}{2}$ .

$y \leq N o (Min i m u m)$

Step 4