We know that when x = 5, | 5 | will also equal 5, but it is also true that | -5 | will equal 5. Before we can embark on solving absolute value equations, let’s take a review of what the word absolute value mean. Show Mobile Notice Show All Notes Hide All Notes. For example |3| = 3 and |-5| = 5. For example, the absolute value of number 5 is written as, |5| = 5. The absolute value of a number can be thought of as the value of the number without regard to its sign. Even though the numbers –5 and 5 are different, they do have something in common. Now we need to do a little legwork. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. To show we want the absolute value we put "|" marks either side (called "bars"), like these examples: How would we solve them? Work out the following examples. Examples of How to Solve Absolute Value Equations. you are probably on a mobile phone). Example  (1.1)  shows that a general case of  | x |  =  a,    is solved by    x  =  +a. |2x + 3| = 5. Solve Equations that Contain Fractions - Example 2. The questions can sometimes appear intimidating, but they're really not as tough as they sometimes first seem. Solve Equations with Absolute Value. https://www.onlinemathlearning.com/equations-absolute-value.html Notes Practice Problems Assignment Problems. Home / Algebra / Solving Equations and Inequalities / Absolute Value Equations. Solve for the real numbers of x in each of the following equations: Solving Absolute Value Equations – Methods & Examples. Absolute value refers to the distance of a point from zero or origin on the number line, regardless of the direction. When solving absolute value equations examples such as this one, look to get the absolute value bars by themselves, all on one side of the equals sign. Examples Solving basic absolute value equations Examples continued More Examples Solving absolute value equations when there are terms outside the symbols Even More Examples Summary/Reflection What is the difference between solving a regular equation and solving an equation where the variable is in an absolute value? You must be logged in to bookmark a video. Solve for all real values of x such that | 3x – 4 | – 2 = 3. Other examples of absolute values of numbers include: |− 9| = 9, |0| = 0, − |−12| = −12 etc. To do this, I create two new equations, where the only difference between then is the sign on the right-hand side. Find out more here about permutations without repetition. Combination Formula, Combinations without Repetition. Remember: Distance can never be negative; therefore, the absolute value of a number is always positive. For example, \(|x−3|=|2x+1|\). The inequality $$\left | x \right |<2$$ Represents the distance between x and 0 that is less than 2. Solving Absolute Value Equations Johnny Wolfe www.BeaconLC.org Jay High School Santa Rosa County Florida September 22, 2001 Solving Absolute Value Equations Examples 1. BACK; NEXT ; Example 1. If two algebraic expressions are equal in absolute value, then they are either equal to each other or negatives of each other. Example (Click to try) 3|2x+1|+4=25 About absolute value equations. They are the same distance from 0 on the number line, but in opposite directions. You da real mvps! First Name Last Name Email Password Join I have an account. To show we want the absolute value we put "|" marks either side (called "bars"), like these examples: Julie S. Syracuse University Add to Playlist. The first thing we’ll talk about are absolute value equations. For example: Notes Practice Problems Assignment Problems. The absolute value of a number may be thought of as its distance from zero. Solve Equations that Contain Fractions - Example 1. You must be logged in to bookmark a video. You may need to review the lesson about how to solve absolute value equations and absolute value inequalities . 3x + 9 = 15. Equations with Absolute Value: Lesson 2 of 2. Isolate the absolute value expression by applying the Law of equations. Isolate the equation with absolute function by add 2 to both sides. This means, we add 5 to both sides of the equation to obtain; Calculate for the positive version of the equation. Mobile Notice. How do you solve an equation with an absolute value? The first answer comes from keeping the inside of the absolute value the same, and solving. We say that –5 and 5 have the same absolute value. Solving equations involving multiple absolute values. If the Absolute Value equals a positive number, then find the distance from both the left and right side by using SCAM again to obtain two solutions. 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