# Tagged Questions

231 views

### inequality method of solution

Im looking for an efficent method of solving the following inequality: $$\left(\frac{x-3}{x+1}\right)^2-7 \left|\frac{x-3}{x+1}\right|+ 10 <0$$ I've tried first determining when the absolute value ...
109 views

### How to show $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$?

I was trying to solve $\log_2 x \cdot \log_{0.25} x \cdot \log_{0.125} x \cdot \log_{16} x > \frac {2}3$ and I keep getting a partial answer of $x>4$ though answer key suggests a more expanded ...
62 views

### solving the inequalty

are there any ways to solve :$x^4 -6x^3 +28x^2 -64x +96 >0$ ?
34 views

### $f(x)=sec(x)$ inequality inconsistency\trouble

I'm currently attempting to find the range of $f(x)=\sec(x)$ by considering $\cos(x)$ in the intervals of $0<\cos(x)\leqslant 1$ and $-1\leqslant \cos(x)<0$ (as $\sec(x)$ is undefined for ...
25 views

### Solving $x^2 - 16 > 0$ for $x$
This may be a very simple question, but I can't figure out the correct reason behind it. If $x^2 - 16 >0$, which of the following must be true? a. $4 < x$ b. $-4 > x > 4$ ...