Absolute Value: The "Extraneous Solution" Trap!

Added: 2026-05-17

[00:00:00]Most people fail this absolute value problem because they forget one crucial step. Let's find out why.

[00:00:06]To solve this, we have to split it into two cases, the positive and the negative.

[00:00:12]In case one, we solve the positive version, which gives us a potential answer of x equal -6.

[00:00:19]In case two, we set the equation to the negative of the right side. Solving that gives us x = 0.8.

[00:00:26]So, we have two possible solutions, -6 and 0.8. But, here is where most students get stuck. We have to check both solutions.

[00:00:36]If we plug in x = -6 into the equation, we get the absolute value of -17 = -17.

[00:00:43]But, absolute value can never be negative. So, 17 does not equal -17.

[00:00:48]That's false.

[00:00:52]Now, let's try 0.8. Plugging it in the equation, we get the absolute value of -3.4 = 3.4. Since 3.4 = 3.4, this statement is true.

[00:01:08]Our only real solution is 0.8 or 4/5.

[00:01:13]The big lesson here, in absolute value, some solutions are extraneous. They look right on paper, but fail the logic test.

[00:01:21]Always check your work.