Finite Math Examples

$x + y < 100$ , $x \cdot 2 + y \cdot 3 < 50$

Step 1

Subtract $y$ from both sides of the inequality.

$x < 100 - y$ and $x \cdot 2 + y \cdot 3 < 50$

Step 2

Simplify the second inequality.

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $2$ to the left of $x$ .

$x < 100 - y$ and $2 \cdot x + y \cdot 3 < 50$

Step 2.1.2

Move $3$ to the left of $y$ .

$x < 100 - y$ and $2 x + 3 y < 50$

Step 2.2

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

$x < 100 - y$ and $2 x < 50 - 3 y$

Step 2.3

Divide each term in $2 x < 50 - 3 y$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 x < 50 - 3 y$ by $2$ .

$x < 100 - y$ and $\frac{2 x}{2} < \frac{50}{2} + \frac{- 3 y}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$x < 100 - y$ and $\frac{2 x}{2} < \frac{50}{2} + \frac{- 3 y}{2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x < 100 - y$ and $x < \frac{50}{2} + \frac{- 3 y}{2}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Divide $50$ by $2$ .

$x < 100 - y$ and $x < 25 + \frac{- 3 y}{2}$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$x < 100 - y$ and $x < 25 - \frac{3 y}{2}$

Step 3