Finite Math Examples

$- x - 2 y < - 2$

Step 1

Add $2 y$ to both sides of the inequality.

$- x < - 2 + 2 y$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 2$ by $- 1$ .

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

Step 2.3.1.2

Move the negative one from the denominator of $\frac{2 y}{- 1}$ .

$x > 2 - 1 \cdot (2 y)$

Step 2.3.1.3

Rewrite $- 1 \cdot (2 y)$ as $- (2 y)$ .

$x > 2 - (2 y)$

Step 2.3.1.4

Multiply $2$ by $- 1$ .

$x > 2 - 2 y$

Step 3

Convert the inequality to interval notation.

$(2 - 2 y, \infty)$

Step 4