Algebra Examples

$y \leq - x - 2$ $y \geq - 5 x + 2$

Step 1

Simplify the first inequality.

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Step 1.1

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

$- x - 2 \geq y$

Step 1.2

Add $2$ to both sides of the inequality.

$- x \geq y + 2$

Step 1.3

Divide each term in $- x \geq y + 2$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- x \geq y + 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{y}{- 1} + \frac{2}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{y}{- 1} + \frac{2}{- 1}$

Step 1.3.2.2

Divide $x$ by $1$ .

$x \leq \frac{y}{- 1} + \frac{2}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative one from the denominator of $\frac{y}{- 1}$ .

$x \leq - 1 \cdot y + \frac{2}{- 1}$

Step 1.3.3.1.2

Rewrite $- 1 \cdot y$ as $- y$ .

$x \leq - y + \frac{2}{- 1}$

Step 1.3.3.1.3

Divide $2$ by $- 1$ .

$x \leq - y - 2$

Step 2

Simplify the second inequality.

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Step 2.1

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

$- 5 x + 2 \leq y$

Step 2.2

Subtract $2$ from both sides of the inequality.

$- 5 x \leq y - 2$

Step 2.3

Divide each term in $- 5 x \leq y - 2$ by $- 5$ and simplify.

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Step 2.3.1

Divide each term in $- 5 x \leq y - 2$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{y}{- 5} + \frac{- 2}{- 5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{y}{- 5} + \frac{- 2}{- 5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{y}{- 5} + \frac{- 2}{- 5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Move the negative in front of the fraction.

$x \geq - \frac{y}{5} + \frac{- 2}{- 5}$

Step 2.3.3.1.2

Dividing two negative values results in a positive value.

$x \geq - \frac{y}{5} + \frac{2}{5}$

Step 3