Pre-Algebra Examples

$2 (y + 4) < - x$

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

Divide each term in $2 (y + 4) < - x$ by $2$ and simplify.

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Step 1.1.1.1

Divide each term in $2 (y + 4) < - x$ by $2$ .

$\frac{2 (y + 4)}{2} < \frac{- x}{2}$

Step 1.1.1.2

Simplify the left side.

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Step 1.1.1.2.1

Cancel the common factor of $2$ .

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Step 1.1.1.2.1.1

Cancel the common factor.

$\frac{2 (y + 4)}{2} < \frac{- x}{2}$

Step 1.1.1.2.1.2

Divide $y + 4$ by $1$ .

$y + 4 < \frac{- x}{2}$

Step 1.1.1.3

Simplify the right side.

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Step 1.1.1.3.1

Move the negative in front of the fraction.

$y + 4 < - \frac{x}{2}$

Step 1.1.2

Subtract $4$ from both sides of the inequality.

$y < - \frac{x}{2} - 4$

Step 1.2

Reorder terms.

$y < - (\frac{1}{2} x) - 4$

Step 1.3

Remove parentheses.

$y < - \frac{1}{2} x - 4$

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 $y = m x + b$ .

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

$b = - 4$

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: $(0, - 4)$

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

y-intercept: $(0, - 4)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- \frac{1}{2} x - 4$ .

$y < - \frac{1}{2} x - 4$

Step 4