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A clear, thorough and complete run down of everything you need to know about the solving equations with the modulus function (absolute value) and the effects of applying it to functions. If you find this content useful, please consider subscribing for more of this kind of content! 0:00 Intro 1:11 Modulus definitions for variables and functions 3:16 Three cases for applying the modulus function and a look at their graphs 3:23 First case where y = |f(x)| 4:49 Second case where y = f(|x|) 6:20 Third case where y = |f(-x)| 8:16 The 3 steps for solving equations with the modulus function applied 10:05 Example of applying the 3 steps to solve |x² - 9| = 7 10:30 First step - Drawing the graphs & identifying the solutions 12:43 Second step - Identifying ranges of x for where f(x) is positive & negative 14:33 Third Step - Identifying & solving equations for ranges of x found in Second step 17:25 Summary If you find this content useful, please consider subscribing for more of this kind of content 🙂 Any feedback or requests left in the comments below will be greatly appreciated. If there are any other topics you would like to see please let me know in thee comments and I will add them to my list of videos! Please consider supporting the channel by giving a small monthly donation. All donations, however small, provide a great deal of support which will allow my to release more videos, more often to help people like you, from all around the world, have access to engaging videos through which to learn a wide range of topics in Mathematics. Please see my patreon page below for more details including benefits for my patreon members! / doseofmath