Algebra Examples

$3 x \geq 12 - 6 y$

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

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

$12 - 6 y \leq 3 x$

Step 1.1.2

Subtract $12$ from both sides of the inequality.

$- 6 y \leq 3 x - 12$

Step 1.1.3

Divide each term in $- 6 y \leq 3 x - 12$ by $- 6$ and simplify.

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Step 1.1.3.1

Divide each term in $- 6 y \leq 3 x - 12$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 y}{- 6} \geq \frac{3 x}{- 6} + \frac{- 12}{- 6}$

Step 1.1.3.2

Simplify the left side.

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Step 1.1.3.2.1

Cancel the common factor of $- 6$ .

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Step 1.1.3.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} \geq \frac{3 x}{- 6} + \frac{- 12}{- 6}$

Step 1.1.3.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{3 x}{- 6} + \frac{- 12}{- 6}$

Step 1.1.3.3

Simplify the right side.

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Step 1.1.3.3.1

Simplify each term.

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Step 1.1.3.3.1.1

Cancel the common factor of $3$ and $- 6$ .

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Step 1.1.3.3.1.1.1

Factor $3$ out of $3 x$ .

$y \geq \frac{3 (x)}{- 6} + \frac{- 12}{- 6}$

Step 1.1.3.3.1.1.2

Cancel the common factors.

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Step 1.1.3.3.1.1.2.1

Factor $3$ out of $- 6$ .

$y \geq \frac{3 x}{3 \cdot - 2} + \frac{- 12}{- 6}$

Step 1.1.3.3.1.1.2.2

Cancel the common factor.

$y \geq \frac{3 x}{3 \cdot - 2} + \frac{- 12}{- 6}$

Step 1.1.3.3.1.1.2.3

Rewrite the expression.

$y \geq \frac{x}{- 2} + \frac{- 12}{- 6}$

Step 1.1.3.3.1.2

Move the negative in front of the fraction.

$y \geq - \frac{x}{2} + \frac{- 12}{- 6}$

Step 1.1.3.3.1.3

Divide $- 12$ by $- 6$ .

$y \geq - \frac{x}{2} + 2$

Step 1.2

Reorder terms.

$y \geq - (\frac{1}{2} x) + 2$

Step 1.3

Remove parentheses.

$y \geq - \frac{1}{2} x + 2$

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 $y = m x + b$ .

$m = - \frac{1}{2}$

$b = 2$

Step 2.2

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $- \frac{1}{2} x + 2$ .

$y \geq - \frac{1}{2} x + 2$

Step 4