Pre-Algebra Examples

$- 2 x - 6 y > - 12$

Step 1

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

Tap for more steps...

Step 1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1

Add $2 x$ to both sides of the inequality.

$- 6 y > - 12 + 2 x$

Step 1.1.2

Divide each term in $- 6 y > - 12 + 2 x$ by $- 6$ and simplify.

Tap for more steps...

Step 1.1.2.1

Divide each term in $- 6 y > - 12 + 2 x$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.2.1

Cancel the common factor of $- 6$ .

Tap for more steps...

Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.2.3.1.1

Divide $- 12$ by $- 6$ .

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

Step 1.1.2.3.1.2

Cancel the common factor of $2$ and $- 6$ .

Tap for more steps...

Step 1.1.2.3.1.2.1

Factor $2$ out of $2 x$ .

$y < 2 + \frac{2 (x)}{- 6}$

Step 1.1.2.3.1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.1.2.3.1.2.2.1

Factor $2$ out of $- 6$ .

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

Step 1.1.2.3.1.2.2.2

Cancel the common factor.

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

Step 1.1.2.3.1.2.2.3

Rewrite the expression.

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

Step 1.1.2.3.1.3

Move the negative in front of the fraction.

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

Step 1.2

Rearrange terms.

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

Step 1.3

Reorder terms.

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

Step 1.4

Remove parentheses.

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

Step 2

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

Tap for more steps...

Step 2.1

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

$m = - \frac{1}{3}$

$b = 2$

Step 2.2

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{3}$

y-intercept: $(0, 2)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{3} x + 2$ .

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

Step 4