Finite Math Examples

$4 x + 3 y > 12$ , $3 x - 4 y < 12$

Step 1

Simplify the first inequality.

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Step 1.1

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

$4 x > 12 - 3 y$ and $3 x - 4 y < 12$

Step 1.2

Divide each term in $4 x > 12 - 3 y$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x > 12 - 3 y$ by $4$ .

$\frac{4 x}{4} > \frac{12}{4} + \frac{- 3 y}{4}$ and $3 x - 4 y < 12$

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.

$\frac{4 x}{4} > \frac{12}{4} + \frac{- 3 y}{4}$ and $3 x - 4 y < 12$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{12}{4} + \frac{- 3 y}{4}$ and $3 x - 4 y < 12$

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 $4$ .

$x > 3 + \frac{- 3 y}{4}$ and $3 x - 4 y < 12$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x > 3 - \frac{3 y}{4}$ and $3 x - 4 y < 12$

Step 2

Simplify the second inequality.

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Step 2.1

Add $4 y$ to both sides of the inequality.

$x > 3 - \frac{3 y}{4}$ and $3 x < 12 + 4 y$

Step 2.2

Divide each term in $3 x < 12 + 4 y$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x < 12 + 4 y$ by $3$ .

$x > 3 - \frac{3 y}{4}$ and $\frac{3 x}{3} < \frac{12}{3} + \frac{4 y}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x > 3 - \frac{3 y}{4}$ and $\frac{3 x}{3} < \frac{12}{3} + \frac{4 y}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > 3 - \frac{3 y}{4}$ and $x < \frac{12}{3} + \frac{4 y}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $12$ by $3$ .

$x > 3 - \frac{3 y}{4}$ and $x < 4 + \frac{4 y}{3}$

Step 3