Finite Math Examples

$2 x + 3 y \leq 12$ , $2 x + y \leq 8$

Step 1

Solve $2 x + 3 y \leq 12$ for $y$ .

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Step 1.1

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

$3 y \leq 12 - 2 x$

Step 1.2

Divide each term in $3 y \leq 12 - 2 x$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 y \leq 12 - 2 x$ by $3$ .

$\frac{3 y}{3} \leq \frac{12}{3} + \frac{- 2 x}{3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} \leq \frac{12}{3} + \frac{- 2 x}{3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{12}{3} + \frac{- 2 x}{3}$

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 $3$ .

$y \leq 4 + \frac{- 2 x}{3}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y \leq 4 - \frac{2 x}{3}$

Step 2

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

$y \leq 8 - 2 x$

Step 3

Find the intersection of $y \leq 4 - \frac{2 x}{3}$ and $y \leq 8 - 2 x$ .

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

Step 4