Algebra Examples

$x - 3 y > 6$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $x$ from both sides of the inequality.

$- 3 y > 6 - x$

Step 1.2

Divide each term in $- 3 y > 6 - x$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 y > 6 - x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} < \frac{6}{- 3} + \frac{- x}{- 3}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} < \frac{6}{- 3} + \frac{- x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{6}{- 3} + \frac{- x}{- 3}$

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 $6$ by $- 3$ .

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 2

Rearrange terms.

$y < \frac{x}{3} - 2$

Step 3

Reorder terms.

$y < \frac{1}{3} x - 2$