Algebraic Inequalities

Solve the inequality $\sqrt{2x-3}<x-1$

Solve the inequality $\sqrt{x+3}<x+3$

Solve the inequality $\sqrt{2x-1}<x-2$

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)

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

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

If the solution set of the quadratic inequality $4x^2<x$ is $\left(a,b\right)$ then find the value of $a+b$.

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 quadratic inequality $2x^2-9x-5<0$ is of the form $\left(a,b\right)$, then find the value of $a+b$.

If the solution set of the quadratic inequality $4x^2-25>0$ is $\left(-\infty , -a\right)\cup \left(a,\infty \right)$, then find the value of $a$.

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 $a+b$.

The solution set for the inequality $x^3(x-1) (x-2) > 0$ is

The solution set for the inequality $x^4-5x^2+4\ge 0$ is

If the solution set for the inequality $x(x-2) (x-5) (x+3)>0$ 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 $\frac{x^2+x+1}{x^2+2}<\frac{1}{3}$ is