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Trouble With Absolute Values

Show Answer If the equations are overlapping the text (they are probably all shifted downwards from where they should be) then you are probably using Internet Explorer 10 or Internet Explorer Having solutions (and for many instructors even just having the answers) readily available would defeat the purpose of the problems. Remember, up here we said, what are the x's that are exactly 10 away from positive 5? Let's say I take the absolute value of negative 1. weblink

So how many numbers that are exactly 10 away from 5? So this graph looks like this strange v. It's kind of hard to find the potential typo if all you write is "The 2 in problem 1 should be a 3" (and yes I've gotten handful of typo reports Now, when x plus 3 is less than 0.

Example 2. Let's see. And so if we write |x − 2| = 4 we mean that x is 4 units aways from 2.

My Students - This is for students who are actually taking a class from me at Lamar University. Let's try to graph one of these, just for fun. The sense will change. 5 > x > −4. If we subtract 3 from both sides, when x is less than negative 3.

Notice that this does require the b be a positive number.  We will deal with what happens if b is zero or negative in a bit. Skip to main contentSubjectsMath by subjectEarly mathArithmeticPre-algebraAlgebraGeometryTrigonometryPrecalculusStatistics & probabilityCalculusDifferential equationsLinear algebraMath for fun and gloryMath by gradeKindergarten1st2nd3rd4th5th6th7th8thHigh schoolScience & engineeringPhysicsChemistryOrganic chemistryBiologyHealth & medicineElectrical engineeringCosmology & astronomyComputingComputer programmingComputer scienceHour of CodeComputer animationArts Put Internet Explorer 11 in Compatibility Mode Look to the right side edge of the Internet Explorer window. Example 4.

Or the thing inside of the absolute value sign, the x plus 2, could also be negative 6. So let's just figure out what this graph would look like in general. All that we need to do is identify the point on the number line and determine its distance from the origin.  Note as well that we also have . Negative 5 minus 5 is negative 10.

Example 1  Solve each of the following. (a)    [Solution] (b)    [Solution] (c)    [Solution] Solution Now, remember that absolute value does not just make all minus signs into plus signs!  To solve Where are the answers/solutions to the Assignment Problems? d) |x − 5| ≤ 2 x is less than or equal to 2 units away from 5. What values could a have?

And it's going to be 4, or negative 8. have a peek at these guys Please post your question on our S.O.S. c) |x + 3| = 1 x is 1 unit away from −3. In this case, as you can see below: ...the two lines, y1 = | x | and y2 = 3, cross at two x-values: x = –3 and x = 3.

FAQ - A few frequently asked questions. If this whole thing evaluated to negative 6, you take the absolute value, you'd get 6. Also, when I first started this site I did try to help as many as I could and quickly found that for a small group of people I was becoming a check over here x > 5 or x < −5.

Let me draw my axes. x falls within d units of 5. Note that these are identical to those in the "Site Help" menu.

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Either that argument will be 8, or it will be −8. Negative 9/2 times 4. We do need to be careful however to not misuse either of these definitions.  For example we can’t use the definition on because we don’t know the value of Once again, you'll get a 19.

It’s now time to start thinking about how to solve equations that contain absolute values.  Let’s start off fairly simple and look at the following equation. a) |x| = 2 x is 2 units away from 0. Problem 16.|x − 5| < d. this content Request Permission for Using Notes - If you are an instructor and wish to use some of the material on this site in your classes please fill out this form.

Here is the purely algebraic definition of |x|: If x ≥ 0, then |x| = x; if x < 0, then |x| = −x. And notice, both of these numbers are exactly 10 away from the number 5. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer. This is asking, what is exactly 6 away from negative 2?

You could try those numbers out for yourself. Two. Algebra/Trig Review Common Math Errors Complex Number Primer How To Study Math Close the Menu Current Location : Algebra (Notes) / Solving Equations and Inequalities / Absolute Value Equations Algebra [Notes] Most of the classes have practice problems with solutions available on the practice problems pages.

So when x is less than negative 3-- that's x is equal to negative 3 right there-- when x is less than negative 3, it looks like this purple graph. If you're seeing this message, it means we're having trouble loading external resources on our website.