So, I think I understand the concept. It's saying that if x is within a certain range of above or below the value which it is approaching (the delta part), then f(x) will be within a certain a certain range of the limit (the epsilon part). But his one in particular is a little tricky for me.

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epsilon = .5

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The problem is:

lim as x is approaching 4 of: 9-x

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The limit is 5, so:

IF the abs. value of x-4 is less than delta,

THEN the abs. value of 9-x-5 is less than epsilon.

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I start with the abs. value of 9-x-5 and try to make it the abs. value of x-4

abs. val. 9-x-5 < eps.

abs. val. -x-4 < eps. (This is where I don't know what to do.)

I've tried factoring out an abs. val. of -1

(abs. val. -1)(abs. val. x 4) < eps.

Then dividing by that abs. val. -1

but then I get, (abs. val. x 4) < eps.

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I'm stuck on how to get it to x-4 and not x 4, if I multiply by -1 then it just goes back to abs. val. -x-4

I'm sure I'm going to facepalm when someone shows me what I'm doing wrong.

Much thanks in advance.