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# Solving absolute value inequalities: no solution

## Video transcript

we're told to solve for y and we have this inequality that says that the absolute value of y plus 22 is less than or equal to 13 and a half or thirteen point five so a good place to start is maybe they just isolate the absolute value of y on the left hand side of this inequality and the best way to do that we can subtract 22 from both sides so let's subtract 22 from both sides the left hand side these guys cancel out that was the whole point so you're just left with the absolute value of y is being less than or equal to and then 13.5 minus 22 let me do it over here 13.5 minus 22 I my brain imagines or the way I processes it I say well that's I always like to put that the larger number first so I say that's the negative of 22 minus 13 point 5 and 22 minus 14 is 8 so or the difference between 22 and 14 is 8 so the difference between 22 and 13 1/2 is going to be 1/2 more than that so this is going to be this right here is eight point five so it's going to be negative eight point five negative eight point five so we get the absolute value of y is less than or equal to negative eight point five now this should cause you some pause because when you take the absolute value of anything what do you know you're going to get if I tell you if I tell you that the absolute value of I don't know any number well we'll just say the absolute value of a is equal to X what do you know about X you know that X is non-negative X non-negative it's either a positive number or 0 here we're saying that Y is let the absolute value when we take the absolute value it has to be less than or equal to a negative number it's saying that it has to be a negative number this is saying this is implicitly saying that Y that the absolute value of y the absolute value of Y has to be negative it not only has to be negative it has to be less than or equal to negative eight point five we know that you take the absolute value of anything you're going to get zero or positive number you non-negative number there is no number you can put here whose absolute values gonna give you a negative number especially one less than negative 8.5 so there is no solution to this problem you cannot find a Y that will satisfy this so there is no solution no solution