Finite Math Examples

$10 x + 6 y < 30$

Step 1

Subtract $6 y$ from both sides of the inequality.

$10 x < 30 - 6 y$

Step 2

Divide each term in $10 x < 30 - 6 y$ by $10$ and simplify.

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Step 2.1

Divide each term in $10 x < 30 - 6 y$ by $10$ .

$\frac{10 x}{10} < \frac{30}{10} + \frac{- 6 y}{10}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} < \frac{30}{10} + \frac{- 6 y}{10}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{30}{10} + \frac{- 6 y}{10}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $30$ by $10$ .

$x < 3 + \frac{- 6 y}{10}$

Step 2.3.1.2

Cancel the common factor of $- 6$ and $10$ .

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Step 2.3.1.2.1

Factor $2$ out of $- 6 y$ .

$x < 3 + \frac{2 (- 3 y)}{10}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $10$ .

$x < 3 + \frac{2 (- 3 y)}{2 (5)}$

Step 2.3.1.2.2.2

Cancel the common factor.

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

Step 2.3.1.2.2.3

Rewrite the expression.

$x < 3 + \frac{- 3 y}{5}$

Step 2.3.1.3

Move the negative in front of the fraction.

$x < 3 - \frac{3 y}{5}$

Step 3

Convert the inequality to interval notation.

$(- \infty, 3 - \frac{3 y}{5})$

Step 4