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We're told to solve for y, and we have this inequality that

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says that the absolute value of y plus 22 is less than or

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equal to 13 and 1/2 or 13.5.

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So a good place to start is maybe to just isolate the

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absolute value of y on the left-hand side of this

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inequality.

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And the best way to do that, we can subtract

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22 from both sides.

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So let's subtract 22 from both sides.

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The left-hand side, these guys cancel out, that was the whole

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point, so you're just left with the absolute value of y

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as being less than or equal to.

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And then 13.5 minus 22, let me do it over

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here, 13.5 minus 22.

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My brain imagines, or the way I process it is, I say, well--

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I always like to put the larger number first-- I say

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that's the negative of 22 minus 13.5.

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And 22 minus 14 is 8, or the difference between 22 and 14

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is 8, so the difference between 22 and 13 and 1/2 is

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going to be 1/2 more than that.

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So this is going to be 8.5.

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So it's going to be negative 8.5.

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So we get the absolute value of y is less than or equal to

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negative 8.5.

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Now, this should cause you some pause, because when you

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take the absolute value of anything, what do you know

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you're going to get?

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If I tell you that the absolute value of any number,

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oh, we'll just say the absolute value of

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a is equal to x.

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What do you know about x?

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You know that x is non-negative.

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It's either a positive number or 0.

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Here we're saying that y is, when we take the absolute

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value, has to be less than or equal to a negative number.

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It's saying that it has to be a negative number.

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This is implicitly saying that the absolute value of y has to

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be negative.

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It not only has to be negative, it has to be less

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than or equal to negative 8.5.

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We know that if you take the absolute value of anything,

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you're going to get 0 or a positive number.

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You're going to get a non-negative number.

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There's no number you can put here whose absolute value's

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going to give you a negative number, especially one less

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than negative 8.5.

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So there is no solution to this problem.

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You cannot find a y that will satisfy this.

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So there is no solution.

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