Algebra Examples

$y > x - 5$ $y \geq - 2 x$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x - 5 < y$ and $y \geq - 2 x$

Step 1.2

Add $5$ to both sides of the inequality.

$x < y + 5$ and $y \geq - 2 x$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x < y + 5$ and $- 2 x \leq y$

Step 2.2

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

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Step 2.2.1

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

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

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.

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

Step 2.2.2.1.2

Divide $x$ by $1$ .

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

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

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

Step 3