# Precalculus Examples

Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Use each root to create test intervals.
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.
Determine if the inequality is true.
Simplify the left side.
Simplify the numerator.
Remove parentheses around .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Remove parentheses around .
Divide by to get .
The left side is greater than the right side , which means that the given statement is always true.
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.
Determine if the inequality is true.
Simplify the left side.
Simplify the numerator.
Remove parentheses around .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Remove parentheses around .
Divide by to get .
The left side is less than the right side , which means that the given statement is false.
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.
Determine if the inequality is true.
Simplify the left side.
Simplify the numerator.
Remove parentheses around .
Subtract from to get .
Simplify the denominator.
Remove parentheses.
Remove parentheses around .
The left side is greater than the right side , which means that the given statement is always true.
True
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
Remove any values from the solution that make the denominator equal to .
or