Why solve inequalities?

Solving inequalities is the last concept you’ll learn in this lesson. Solving them is very similar to solving equations (and you apply largely the same techniques), except now your solutions will involve a range of values. To find this range, you first have to be able to solve equalities, which is why you learned that first.

Before diving into some examples, let’s talk about why being able to solve inequalities is so important.

Solving inequalities is one of many steps needed for graphing. Similar to how you often want to know where a particular function is equal to a particular y-value, you’ll also want to know where functions are greater or less than a particular y-value.

You’ve learned generally that the derivative, f’(x), is the slope of a function f(x) at any x-value. You’ll often want to know where f’(x) > 0—in other words, where the slope is positive—because that means f(x) is increasing. Likewise, you’ll want to know where f’(x) < 0—in other words, where the slope is negative—because that means f(x) is decreasing.