Precalculus Examples

$y - 2 x - 2 < 0$ , $x + y > 2$

Step 1

Simplify the first inequality.

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Step 1.1

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.1.1

Subtract $y$ from both sides of the inequality.

$- 2 x - 2 < - y$ and $x + y > 2$

Step 1.1.2

Add $2$ to both sides of the inequality.

$- 2 x < - y + 2$ and $x + y > 2$

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

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

Dividing two negative values results in a positive value.

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

Step 1.2.3.1.2

Divide $2$ by $- 2$ .

$x > \frac{y}{2} - 1$ and $x + y > 2$

Step 2

Subtract $y$ from both sides of the inequality.

$x > \frac{y}{2} - 1$ and $x > 2 - y$

Step 3