Algebra Examples

$8 x - 3 y < 4$ $9 x + 2 y < - 1$

Step 1

Solve $8 x - 3 y < 4$ for $y$ .

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Step 1.1

Subtract $8 x$ from both sides of the inequality.

$- 3 y < 4 - 8 x$

Step 1.2

Divide each term in $- 3 y < 4 - 8 x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y < 4 - 8 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{4}{- 3} + \frac{- 8 x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{4}{- 3} + \frac{- 8 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y > \frac{4}{- 3} + \frac{- 8 x}{- 3}$

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

Move the negative in front of the fraction.

$y > - \frac{4}{3} + \frac{- 8 x}{- 3}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y > - \frac{4}{3} + \frac{8 x}{3}$

Step 2

Solve $9 x + 2 y < - 1$ for $y$ .

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Step 2.1

Subtract $9 x$ from both sides of the inequality.

$2 y < - 1 - 9 x$

Step 2.2

Divide each term in $2 y < - 1 - 9 x$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 y < - 1 - 9 x$ by $2$ .

$\frac{2 y}{2} < \frac{- 1}{2} + \frac{- 9 x}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} < \frac{- 1}{2} + \frac{- 9 x}{2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 1}{2} + \frac{- 9 x}{2}$

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

Move the negative in front of the fraction.

$y < - \frac{1}{2} + \frac{- 9 x}{2}$

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y < - \frac{1}{2} - \frac{9 x}{2}$

Step 3

Find the intersection of $y > - \frac{4}{3} + \frac{8 x}{3}$ and $y < - \frac{1}{2} - \frac{9 x}{2}$ .

$- \frac{4}{3} + \frac{8 x}{3} < y < - \frac{1}{2} - \frac{9 x}{2}$

Step 4