equal to negative 1/7. There are two ways to define absolute value. That is exactly what this equation is saying however. because we don’t know the value of \(x\). is equal to negative 6 times the absolute value Also, we will always use a positive value for distance. All we need to note is that in the formula above \(p\) represents whatever is on the inside of the absolute value bars and so in this case we have. Do not make the assumption that because the first potential solution is negative it won’t be a solution. Intro to absolute value equations and graphs, Worked example: absolute value equation with two solutions, Worked example: absolute value equations with one solution, Worked example: absolute value equations with no solution. this is the same thing as 1/7. sides by 14 to get rid of that coefficient So, this leads to the following general formula for equations involving absolute value. We will look at both. Since this isn’t possible that means there is no solution to this equation. that for a second. 6 x plus 7's cancel out, or absolute values of That also will guarantee that these two expressions aren’t the same. It is. reason through this? here were equal to 1/7, you take its absolute To log in and use all the features of Khan Academy, please enable JavaScript in your browser. At this point we’ve got two linear equations that are easy to solve. This one will work in pretty much the same way so we won’t put in quite as much explanation. 8 times the absolute value of x plus 7 plus 4-- in that same color-- is equal to negative 6 times the absolute value of x plus 7 plus 6 You have these If there is a negative outside the absolute value bar, it stays there. value of x plus 7, but we really need So we'll divide If this thing right over absolute value problem. Solving Absolute Value Equations Solving absolute value equations is as easy as working with regular linear equations. think about this is if you could solve for the are equal and we are being told They're both divisible by 2, so us to negative 50/7. There is a geometric definition and a mathematical definition. Now, let’s take a look at how to deal with equations for which \(b\) is zero or negative. Donate or volunteer today! Or in other words, we must have, to be equal to 2. So that's one possibility for x. taking the absolute value of-- so x plus 7-- could I took the absolute value of. this equation so that the absolute Phone support is available Monday-Friday, 9:00AM-10:00PM ET. The definitions above are easy to apply if all we’ve got are numbers inside the absolute value bars.

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