Solutions of Linear Inequalities in One Variable

If $\frac{x^2+4x+2}{2x^2-x-1}>0$, then $x\in$

Solve $1+\frac{2}{x-1}⩾\frac{6}{x}$

Largest integral value of $x$ satisfying $\frac{x^2+2x-4}{x^2-4x+5}>3$ is 

If $\frac{\left|x+3\right|+x}{x+2}>1, \text{then} x\in$

Solve: $\left|3x+1\right|\ge \left|2x+1\right|$

Solve,

$\left|\frac{2}{x-4}\right|>1,x\ne 4$

Find the solution set of $x$ if $3x-7>5x -1$
 

$a^2+ax<1-x$ Solve for $x$.

Let $f\left(x\right)=k{x}^2+x\left(3-4k\right)-12.$ If the set of values of $k$ for which $f\left(x\right)<0 \forall x\in \left(-3,3\right)$ and $f\left(-4\right)>0$ is $(p,q]$ then find the value of $4p+3q.$

The set of values of $k\left(k\in R\right),$ for which the equation $x^2-4\left|x\right|+3-\left|k-1\right|=0$ will have exactly four real roots is 

Let $\frac{y+3}{2y+5}={\sin }^{2}x+2\cos x+1, \text{where} x\in R.$ If the range of $y$ is $(-\infty ,a]\cup [b,\infty ),$ then find the value of $\left(3a-5b\right).$

The solution set of the inequality $\frac{1}{x-2}-\frac{1}{x}⩽\frac{2}{x+2}$ is $(-\alpha ,\beta ]\cup \left(\gamma ,\alpha \right)\cup [\delta ,\infty )$ then 

If $\sqrt{n^2+1}=\sqrt{n^2+\gamma }$, where $\mathrm{n},\gamma \in N$. How many different values of $\gamma$ are possible ?

In wavy curve method why does coefficient of $x$ have to be positive$?$

$f\left(x\right)=3x+x^2-\frac{x^3}{3}+7.$ If $\left[a,b\right]$ is the complete solution set for $f\text{'}\left(x\right)⩾0$, then $a+b$ is$?$

Solve for $x, \frac{\left(x-2\right)\left(x-5\right)}{\left(x-3\right)}>0$

Solve for $x, \frac{x-2}{x^2+1}<\frac{-1}{2}$ 

Solve the linear inequality $ax\le 1$.

Solve $\frac{x-2}{x+2}>\frac{2x-3}{4x-1}$

Solve $2+\frac{3}{1+x}\ge \frac{2}{x}$