Solve the following inequality: $\frac{|x+2|-x}{x} < 2$

If $\sqrt{9x^2+6x+1} < (2-x)$,then:

Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.

The value of the greatest integer $k$ satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in \mathbb{N}$ is

The set of all real values of $x$ satisfying the inequalities $x^2-4x+3 > 0$ and $x^2-2x-8 \leq 0$ is

In an experiment,a solution of hydrochloric acid is to be kept between $30^{\circ} \text{C}$ and $35^{\circ} \text{C}$. What is the range of temperature in degree Fahrenheit if the conversion formula is given by $C = \frac{5}{9}(F - 32)$,where $C$ and $F$ represent temperature in degree Celsius and degree Fahrenheit,respectively?