Finite Math Examples

$8 x + 2 y > 16$ , $5 x - 3 y < 15$

Step 1

Simplify the first inequality.

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Step 1.1

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

$8 x > 16 - 2 y$ or $5 x - 3 y < 15$

Step 1.2

Divide each term in $8 x > 16 - 2 y$ by $8$ and simplify.

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Step 1.2.1

Divide each term in $8 x > 16 - 2 y$ by $8$ .

$\frac{8 x}{8} > \frac{16}{8} + \frac{- 2 y}{8}$ or $5 x - 3 y < 15$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} > \frac{16}{8} + \frac{- 2 y}{8}$ or $5 x - 3 y < 15$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{16}{8} + \frac{- 2 y}{8}$ or $5 x - 3 y < 15$

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 $16$ by $8$ .

$x > 2 + \frac{- 2 y}{8}$ or $5 x - 3 y < 15$

Step 1.2.3.1.2

Cancel the common factor of $- 2$ and $8$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 2 y$ .

$x > 2 + \frac{2 (- y)}{8}$ or $5 x - 3 y < 15$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $8$ .

$x > 2 + \frac{2 (- y)}{2 (4)}$ or $5 x - 3 y < 15$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x > 2 + \frac{2 (- y)}{2 \cdot 4}$ or $5 x - 3 y < 15$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x > 2 + \frac{- y}{4}$ or $5 x - 3 y < 15$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$x > 2 - \frac{y}{4}$ or $5 x - 3 y < 15$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x > 2 - \frac{y}{4}$ or $5 x < 15 + 3 y$

Step 2.2

Divide each term in $5 x < 15 + 3 y$ by $5$ and simplify.

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Step 2.2.1

Divide each term in $5 x < 15 + 3 y$ by $5$ .

$x > 2 - \frac{y}{4}$ or $\frac{5 x}{5} < \frac{15}{5} + \frac{3 y}{5}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $5$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x > 2 - \frac{y}{4}$ or $\frac{5 x}{5} < \frac{15}{5} + \frac{3 y}{5}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > 2 - \frac{y}{4}$ or $x < \frac{15}{5} + \frac{3 y}{5}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $15$ by $5$ .

$x > 2 - \frac{y}{4}$ or $x < 3 + \frac{3 y}{5}$

Step 3