**Q: Solve the inequality: 0 < 1/x < 1/5**

A: OK… Start by clearing the denominator… Multiply all sides by x:

0 < 1/x < 1/5

x*0 < x*(1/x) < x*(1/5)

Now, simplify and reduce:

0 < x/x < (1/5)x

0 < 1 < (1/5)x

OK… So look at the left part: 0 < 1!!! We already know that, right?? Hopefully 🙂 So, that part is actually useless to us now. Old news. Don’t need it. What we do need is:

1 < (1/5)x

Multiply both sides by 5:

5*1 < 5 * (1/5) x

Simplify and reduce:

5 < 5/5 x

5 < x

TADA

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