Algebra Examples

$- 3 x + 2 y > 5 y + 9$

Step 1

Move all terms containing $y$ to the left side of the inequality.

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Step 1.1

Subtract $5 y$ from both sides of the inequality.

$- 3 x + 2 y - 5 y > 9$

Step 1.2

Subtract $5 y$ from $2 y$ .

$- 3 x - 3 y > 9$

Step 2

Add $3 x$ to both sides of the inequality.

$- 3 y > 9 + 3 x$

Step 3

Divide each term in $- 3 y > 9 + 3 x$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y > 9 + 3 x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} < \frac{9}{- 3} + \frac{3 x}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} < \frac{9}{- 3} + \frac{3 x}{- 3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y < \frac{9}{- 3} + \frac{3 x}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Divide $9$ by $- 3$ .

$y < - 3 + \frac{3 x}{- 3}$

Step 3.3.1.2

Cancel the common factor of $3$ and $- 3$ .

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Step 3.3.1.2.1

Factor $3$ out of $3 x$ .

$y < - 3 + \frac{3 (x)}{- 3}$

Step 3.3.1.2.2

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

$y < - 3 - 1 \cdot x$

Step 3.3.1.3

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

$y < - 3 - x$