# Precalculus Examples

Step 1
Convert the inequality to an equation.
Step 2
Add to both sides of the equation.
Step 3
Factor using the AC method.
Step 3.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.2
Write the factored form using these integers.
Step 4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5
Set equal to and solve for .
Step 5.1
Set equal to .
Step 5.2
Add to both sides of the equation.
Step 6
Set equal to and solve for .
Step 6.1
Set equal to .
Step 6.2
Add to both sides of the equation.
Step 7
The final solution is all the values that make true.
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.
Step 9.1
Test a value on the interval to see if it makes the inequality true.
Step 9.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.1.2
Replace with in the original inequality.
Step 9.1.3
The left side is greater than the right side , which means that the given statement is false.
False
False
Step 9.2
Test a value on the interval to see if it makes the inequality true.
Step 9.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.2.2
Replace with in the original inequality.
Step 9.2.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 9.3
Test a value on the interval to see if it makes the inequality true.
Step 9.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 9.3.2
Replace with in the original inequality.
Step 9.3.3
The left side is greater than the right side , which means that the given statement is false.
False
False
Step 9.4
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
Step 10
The solution consists of all of the true intervals.
Step 11
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 12