Wavy Curve Method

The set of all solution of inequality $\frac{\left(e^x-1\right)(2x-3)\left(x^2+x+2\right)}{(\sin x-\sqrt{5})(x+1)x}\le 0$ is

Complete solution set of inequalities $1\le \frac{x+1}{2x-1}<2$ is

Solution set for the in equation $\frac{x^2-1}{x}\le 2-x$ is

Set of all values of $x$, satisfying the inequality $x-3<\sqrt{x^2+4x-5}$

Complete solution set of inequalities $1\le \frac{x+1}{2x-1}<2$ is

The value of $x$ satisfying $\frac{{\left(x^2+2\right)}^5{\left(x-1\right)}^4{\left(x-4\right)}^7}{\left(x^2-2x+10\right){\left(x-2\right)}^6\left(x-5\right)}\ge 0$ is  

If $x^2+6x-27>0$ and $x^2-3x-4<0$, then 

Integers satisfying the inequalities $x^2+9<{\left(x+3\right)}^2<8x+25$ is(are)

The values of $x$ satisfying$5x-1< {\left(x+1\right)}^2<7x-3$ is(are)

Find the sum of all the real solutions of the inequality $\frac{\left(x^2+2\right)\left(\sqrt{x^2-16}\right)}{\left(x^4+2\right)\left(x^2-9\right)}\le 0$.

If $\left(1+\sqrt{2}\right)$ is a root of the equation $x-\frac{1}{x}=k$ where $k$ is a constant, find the value of $k$

The solution of ${\log }_{0.5}\left({\log }_2\frac{x^2+1}{\left|x-1\right|}\right)<0$ is

The value of $x$ satisfying $\frac{{\left(x^2+2\right)}^5{\left(x-1\right)}^4{\left(x-4\right)}^7}{\left(x^2-2x+10\right){\left(x-2\right)}^6\left(x-5\right)}\ge 0$ is  

The solution set for the inequality $\frac{x^2+3x+2}{x^2-16}\ge 0$ is 

If the solution set for the inequality $x(x-3) (x-5) (x+4)>0$ is of the form $(-\infty ,a)\cup (0,b)\cup \left(c,\infty \right)$ then find the value of $a+b+c$.

The solution set for the inequality $\frac{\left(x+1\right) (x-3)}{x+2}\le 0$ is

If the solution set of quadratic inequality $x^2-x-6<0$ is of the form $\left(a,b\right)$, then find the value of $a+b$.

If the solution set of quadratic inequality $-x^2+3x-2\ge 0$ is of the form $\left[a,b\right]$, then find the value of $a+b$.

If the solution set of the inequality $x^2(x-1) (x-2)\le 0$ is of the form $\left\{0\right\}\cup \left[a,b\right]$, then find the value of $a+b$.