Question

Solve the inequality
\[\large\rm -1<\frac{2cos x }{√3}<1 \]

Answer 1

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Answer 2

hint: rearrange the inequality to just have cosx in the middle

Answer 3

I can solve it till the end but why does then sign changes at the end?

Answer 4

well if you want an x, you have written it as A < f(x) < B
so this becomes f(x) > A and f(x) < B
So the sign change for the lower inequality is really making the subject appear first.

Note in this situation, have they stated a domain for x? If not, then you could write it up as a general solution, which is a bit trickier.