Finite Math Examples

$6 y < - 10 x + 24$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- 10 x + 24 > 6 y$

Step 2

Subtract $24$ from both sides of the inequality.

$- 10 x > 6 y - 24$

Step 3

Divide each term in $- 10 x > 6 y - 24$ by $- 10$ and simplify.

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Step 3.1

Divide each term in $- 10 x > 6 y - 24$ by $- 10$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 10 x}{- 10} < \frac{6 y}{- 10} + \frac{- 24}{- 10}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 10$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} < \frac{6 y}{- 10} + \frac{- 24}{- 10}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{6 y}{- 10} + \frac{- 24}{- 10}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

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

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Step 3.3.1.1.1

Factor $2$ out of $6 y$ .

$x < \frac{2 (3 y)}{- 10} + \frac{- 24}{- 10}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $- 10$ .

$x < \frac{2 (3 y)}{2 (- 5)} + \frac{- 24}{- 10}$

Step 3.3.1.1.2.2

Cancel the common factor.

$x < \frac{2 (3 y)}{2 \cdot - 5} + \frac{- 24}{- 10}$

Step 3.3.1.1.2.3

Rewrite the expression.

$x < \frac{3 y}{- 5} + \frac{- 24}{- 10}$

Step 3.3.1.2

Move the negative in front of the fraction.

$x < - \frac{3 y}{5} + \frac{- 24}{- 10}$

Step 3.3.1.3

Cancel the common factor of $- 24$ and $- 10$ .

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Step 3.3.1.3.1

Factor $- 2$ out of $- 24$ .

$x < - \frac{3 y}{5} + \frac{- 2 (12)}{- 10}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

Factor $- 2$ out of $- 10$ .

$x < - \frac{3 y}{5} + \frac{- 2 \cdot 12}{- 2 \cdot 5}$

Step 3.3.1.3.2.2

Cancel the common factor.

$x < - \frac{3 y}{5} + \frac{- 2 \cdot 12}{- 2 \cdot 5}$

Step 3.3.1.3.2.3

Rewrite the expression.

$x < - \frac{3 y}{5} + \frac{12}{5}$