# Calculus Examples

Step 1
Subtract from both sides of the inequality.
Step 2
Simplify .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Subtract from .
Step 3
Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Step 4
Subtract from both sides of the equation.
Step 5
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Step 6
Consolidate the solutions.
Step 7
Find the domain of .
Set the denominator in equal to to find where the expression is undefined.
The domain is all values of that make the expression defined.
Step 8
Use each root to create test intervals.
Step 9
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not greater than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
Step 10
The solution consists of all of the true intervals.
or
Step 11
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 12