Finite Math Examples

$3 x + 4 y < 6$ , $2 x - 3 y > 4$

Step 1

Simplify the first inequality.

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Step 1.1

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

$3 x < 6 - 4 y$ and $2 x - 3 y > 4$

Step 1.2

Divide each term in $3 x < 6 - 4 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x < 6 - 4 y$ by $3$ .

$\frac{3 x}{3} < \frac{6}{3} + \frac{- 4 y}{3}$ and $2 x - 3 y > 4$

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.

$\frac{3 x}{3} < \frac{6}{3} + \frac{- 4 y}{3}$ and $2 x - 3 y > 4$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{6}{3} + \frac{- 4 y}{3}$ and $2 x - 3 y > 4$

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 $6$ by $3$ .

$x < 2 + \frac{- 4 y}{3}$ and $2 x - 3 y > 4$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$x < 2 - \frac{4 y}{3}$ and $2 x - 3 y > 4$

Step 2

Simplify the second inequality.

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Step 2.1

Add $3 y$ to both sides of the inequality.

$x < 2 - \frac{4 y}{3}$ and $2 x > 4 + 3 y$

Step 2.2

Divide each term in $2 x > 4 + 3 y$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x > 4 + 3 y$ by $2$ .

$x < 2 - \frac{4 y}{3}$ and $\frac{2 x}{2} > \frac{4}{2} + \frac{3 y}{2}$

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.

$x < 2 - \frac{4 y}{3}$ and $\frac{2 x}{2} > \frac{4}{2} + \frac{3 y}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < 2 - \frac{4 y}{3}$ and $x > \frac{4}{2} + \frac{3 y}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $4$ by $2$ .

$x < 2 - \frac{4 y}{3}$ and $x > 2 + \frac{3 y}{2}$

Step 3