# Tagged Questions

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### Solve the inequality: $|x^2 − 4| < 2$

This is a question on a calculus assignment our class received, I am a little confused on a few parts to the solution, can someone clear a few things up with it? Since $x^2-4 = 0$ that means $x = 2$ ...
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### Writing a proof of an inequality between fractions

I have no idea how to do this. Suppose $x,y,z,n$ are positive integers. Given that $\frac{x}{y} < \frac{z}{n}$, prove that $$\frac{x}{y} < \frac{x+z}{y+n}$$
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### inequalities and their solutions

a. Since: 9|x + 9| + 6 > 5 9|x + 9| > -1 |x + 9| > -1/9 => always true, every real x value is a solution so it has infinitely many solutions. (−∞, ∞) How would I graph this solution set on a ...
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### Solve $\frac{(x - 1)^3(x + 1)^8}{(x + 2)^4} > 0$

Solve the inequality $$\frac{(x - 1)^3(x + 1)^8}{(x + 2)^4} > 0$$ A) $X<1$ B) $X>1$ C) $X>-1$ D) $X<-1$ E) $X>-2$
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### Finding two sided bounds on $(x+y)/(xy)$ given inequalities for $x$ and $y$

Given $\dfrac{1}{6} < x < \dfrac{1}{2}$ and $\dfrac{1}{7} < y < \dfrac{1}{3}$, can we determine bounds for $\dfrac{x+y}{xy}$?
I'm looking for hints on how to efficiently solve this inequality: $$\left( \frac {|x|-|1-x|}{|x|} \right)^{2x-1} \gt \left(\frac {|x|-|1-x|}{|x|} \right)^{8-x}$$