# Precalculus Examples

Convert the inequality to an equation.

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 .

Write the factored form using these integers.

Set the factor equal to .

Add to both sides of the equation.

Set the factor equal to .

Subtract from both sides of the equation.

Consolidate the solutions.

Use each root to create test intervals.

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 less 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 less 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 less than the right side , which means that the given statement is false.

False

False

Compare the intervals to determine which ones satisfy the original inequality.

False

True

False

False

True

False

The solution consists of all of the true intervals.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation: