Pre-Algebra Examples

$f (x) > g (x)$

Step 1

Subtract $f (x)$ from both sides of the inequality.

$0 > g x - f (x)$

Step 2

Find the slope and the y-intercept for the boundary line.

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Step 2.1

Rewrite in slope-intercept form.

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Step 2.1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.1.2

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

$g x - f (x) < 0$

Step 2.1.3

Add $f (x)$ to both sides of the inequality.

$g x < f (x)$

Step 2.1.4

Divide each term in $g x < f (x)$ by $x$ and simplify.

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Step 2.1.4.1

Divide each term in $g x < f (x)$ by $x$ .

$\frac{g x}{x} < \frac{f (x)}{x}$

Step 2.1.4.2

Simplify the left side.

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Step 2.1.4.2.1

Cancel the common factor of $x$ .

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Step 2.1.4.2.1.1

Cancel the common factor.

$\frac{g x}{x} < \frac{f (x)}{x}$

Step 2.1.4.2.1.2

Divide $g$ by $1$ .

$g < \frac{f (x)}{x}$

Step 2.1.5

Rewrite in slope-intercept form.

$= \frac{x}{x} f$

Step 2.2

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $g x - f (x)$ .

$0 > g x - f (x)$

Step 4