Algebra Examples

$y > 3 x - 5$ $y > - x + 2$

Step 1

Simplify the first inequality.

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Step 1.1

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

$3 x - 5 < y$ and $y > - x + 2$

Step 1.2

Add $5$ to both sides of the inequality.

$3 x < y + 5$ and $y > - x + 2$

Step 1.3

Divide each term in $3 x < y + 5$ by $3$ and simplify.

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Step 1.3.1

Divide each term in $3 x < y + 5$ by $3$ .

$\frac{3 x}{3} < \frac{y}{3} + \frac{5}{3}$ and $y > - x + 2$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} < \frac{y}{3} + \frac{5}{3}$ and $y > - x + 2$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{y}{3} + \frac{5}{3}$ and $y > - x + 2$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x < \frac{y}{3} + \frac{5}{3}$ and $- x + 2 < y$

Step 2.2

Subtract $2$ from both sides of the inequality.

$x < \frac{y}{3} + \frac{5}{3}$ and $- x < y - 2$

Step 2.3

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

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Step 2.3.1

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

$x < \frac{y}{3} + \frac{5}{3}$ and $\frac{- x}{- 1} > \frac{y}{- 1} + \frac{- 2}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$x < \frac{y}{3} + \frac{5}{3}$ and $\frac{x}{1} > \frac{y}{- 1} + \frac{- 2}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x < \frac{y}{3} + \frac{5}{3}$ and $x > \frac{y}{- 1} + \frac{- 2}{- 1}$

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

$x < \frac{y}{3} + \frac{5}{3}$ and $x > - 1 \cdot y + \frac{- 2}{- 1}$

Step 2.3.3.1.2

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

$x < \frac{y}{3} + \frac{5}{3}$ and $x > - y + \frac{- 2}{- 1}$

Step 2.3.3.1.3

Divide $- 2$ by $- 1$ .

$x < \frac{y}{3} + \frac{5}{3}$ and $x > - y + 2$

Step 3