Arun Sharma Solutions for Exercise 1: Level of Difficulty

Find the smallest integral $x$ satisfying the inequality $\frac{x-5}{x^2+5x-14}>0$

Find the maximum value of $x$ for which $\frac{x+2}{x}\ge x$

For how many integer values of $x$, is the expression:
$(x-1)(4-x){(x-2)}^2>0$

Find the minimum value of $x$ for which $\frac{1}{x-0.5}<2$ where $x\in I^{+}$

For how many integer values of $x$ is:
$\frac{x^2+6x-7}{x^2+1}>2$

Maximum value of $x$, for which $\frac{x^2-9}{x^2+x+1}\le 0$

If $f\left(x\right)=x^2+2\left|x\right|+1$, then for how many real values of $x$ is $f\left(x\right)\le 0$?

If $\frac{1}{\left|x\right|-2}>\frac{1}{3}$, then the last positive integer value of $x$, for which this inequality is true?