Algebra Examples

$y < - \frac{1}{6} x + 3 y$

Step 1

Write in $y = m x + b$ form.

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Combine $x$ and $\frac{1}{6}$ .

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

Step 1.1.2

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

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Step 1.1.2.1

Subtract $3 y$ from both sides of the inequality.

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

Step 1.1.2.2

Subtract $3 y$ from $y$ .

$- 2 y < - \frac{x}{6}$

Step 1.1.3

Divide each term in $- 2 y < - \frac{x}{6}$ by $- 2$ and simplify.

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Step 1.1.3.1

Divide each term in $- 2 y < - \frac{x}{6}$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{- \frac{x}{6}}{- 2}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $- 2$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{- \frac{x}{6}}{- 2}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y > \frac{- \frac{x}{6}}{- 2}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$y > - \frac{x}{6} \cdot \frac{1}{- 2}$

Step 1.1.3.3.2

Move the negative in front of the fraction.

$y > - \frac{x}{6} (- \frac{1}{2})$

Step 1.1.3.3.3

Multiply $- \frac{x}{6} (- \frac{1}{2})$ .

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Step 1.1.3.3.3.1

Multiply $- 1$ by $- 1$ .

$y > 1 \frac{x}{6} \frac{1}{2}$

Step 1.1.3.3.3.2

Multiply $\frac{x}{6}$ by $1$ .

$y > \frac{x}{6} \cdot \frac{1}{2}$

Step 1.1.3.3.3.3

Multiply $\frac{x}{6}$ by $\frac{1}{2}$ .

$y > \frac{x}{6 \cdot 2}$

Step 1.1.3.3.3.4

Multiply $6$ by $2$ .

$y > \frac{x}{12}$

Step 1.2

Reorder terms.

$y > \frac{1}{12} x$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{1}{12}$

$b = 0$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{12}$

y-intercept: $(0, 0)$

Slope: $\frac{1}{12}$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{1}{12} x$ .

$y > \frac{1}{12} x$

Step 4