Algebra Examples

$- 9 x + 5 y \leq - 6$ $4 x - 8 y < - 16$

Step 1

Solve $- 9 x + 5 y \leq - 6$ for $y$ .

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Step 1.1

Add $9 x$ to both sides of the inequality.

$5 y \leq - 6 + 9 x$

Step 1.2

Divide each term in $5 y \leq - 6 + 9 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y \leq - 6 + 9 x$ by $5$ .

$\frac{5 y}{5} \leq \frac{- 6}{5} + \frac{9 x}{5}$

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.

$\frac{5 y}{5} \leq \frac{- 6}{5} + \frac{9 x}{5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{- 6}{5} + \frac{9 x}{5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$y \leq - \frac{6}{5} + \frac{9 x}{5}$

Step 2

Solve $4 x - 8 y < - 16$ for $y$ .

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Step 2.1

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

$- 8 y < - 16 - 4 x$

Step 2.2

Divide each term in $- 8 y < - 16 - 4 x$ by $- 8$ and simplify.

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Step 2.2.1

Divide each term in $- 8 y < - 16 - 4 x$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 y}{- 8} > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 8$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{- 16}{- 8} + \frac{- 4 x}{- 8}$

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 $- 16$ by $- 8$ .

$y > 2 + \frac{- 4 x}{- 8}$

Step 2.2.3.1.2

Cancel the common factor of $- 4$ and $- 8$ .

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Step 2.2.3.1.2.1

Factor $- 4$ out of $- 4 x$ .

$y > 2 + \frac{- 4 (x)}{- 8}$

Step 2.2.3.1.2.2

Cancel the common factors.

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Step 2.2.3.1.2.2.1

Factor $- 4$ out of $- 8$ .

$y > 2 + \frac{- 4 (x)}{- 4 (2)}$

Step 2.2.3.1.2.2.2

Cancel the common factor.

$y > 2 + \frac{- 4 x}{- 4 \cdot 2}$

Step 2.2.3.1.2.2.3

Rewrite the expression.

$y > 2 + \frac{x}{2}$

Step 3

Find the intersection of $y \leq - \frac{6}{5} + \frac{9 x}{5}$ and $y > 2 + \frac{x}{2}$ .

$2 + \frac{x}{2} < y \leq - \frac{6}{5} + \frac{9 x}{5}$

Step 4