Finite Math Examples

$5 x - 4 y < 20$ , $7 x + 5 y > 35$

Step 1

Simplify the first inequality.

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Step 1.1

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

$5 x < 20 + 4 y$ and $7 x + 5 y > 35$

Step 1.2

Divide each term in $5 x < 20 + 4 y$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 x < 20 + 4 y$ by $5$ .

$\frac{5 x}{5} < \frac{20}{5} + \frac{4 y}{5}$ and $7 x + 5 y > 35$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} < \frac{20}{5} + \frac{4 y}{5}$ and $7 x + 5 y > 35$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{20}{5} + \frac{4 y}{5}$ and $7 x + 5 y > 35$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $20$ by $5$ .

$x < 4 + \frac{4 y}{5}$ and $7 x + 5 y > 35$

Step 2

Simplify the second inequality.

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Step 2.1

Subtract $5 y$ from both sides of the inequality.

$x < 4 + \frac{4 y}{5}$ and $7 x > 35 - 5 y$

Step 2.2

Divide each term in $7 x > 35 - 5 y$ by $7$ and simplify.

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Step 2.2.1

Divide each term in $7 x > 35 - 5 y$ by $7$ .

$x < 4 + \frac{4 y}{5}$ and $\frac{7 x}{7} > \frac{35}{7} + \frac{- 5 y}{7}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $7$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x < 4 + \frac{4 y}{5}$ and $\frac{7 x}{7} > \frac{35}{7} + \frac{- 5 y}{7}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < 4 + \frac{4 y}{5}$ and $x > \frac{35}{7} + \frac{- 5 y}{7}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Divide $35$ by $7$ .

$x < 4 + \frac{4 y}{5}$ and $x > 5 + \frac{- 5 y}{7}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$x < 4 + \frac{4 y}{5}$ and $x > 5 - \frac{5 y}{7}$

Step 3