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. 

In the following video, you’ll see examples that involve solving inequalities. You’ll then have the opportunity to practice.


Lesson 1: The Basics

Lesson 2: Solving equations and inequalities

  1. Why solve equations?
  2. Solving equations: Quadratics
  3. Exercises: Solve quadratic equations
  4. Solving equations: Absolute values
  5. Exercises: Solve equations involving absolute value
  6. Solving equations: Polynomials
  7. Exercises: Solve polynomial equations
  8. Solving equations: Rational expressions
  9. Exercises: Solve equations involving rational expressions
  10. Solving equations: Exponents
  11. Exercises: Solve exponential equations
  12. Solving equations: Logs
  13. Exercises: Solve logarithmic equations
  14. Solving equations: Trigonometric functions
  15. Trig identities
  16. Exercises: Solve trigonometric equations
  17. Why solve inequalities? 📝
  18. Solving inequalities
  19. Exercises: Solve inequalities

Lesson 3: Graphing

Lesson 4: Limits and series

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