Algebra Examples

$x - y \geq 1$ $2 x + y < 2$

Step 1

Solve $x - y \geq 1$ for $y$ .

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Step 1.1

Subtract $x$ from both sides of the inequality.

$- y \geq 1 - x$

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.2.2.2

Divide $y$ by $1$ .

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

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

Divide $1$ by $- 1$ .

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.2.3.1.3

Divide $x$ by $1$ .

$y \leq - 1 + x$

Step 2

Subtract $2 x$ from both sides of the inequality.

$y < 2 - 2 x$

Step 3

Find the intersection of $y \leq - 1 + x$ and $y < 2 - 2 x$ .

$y < N o (Min i m u m)$

Step 4