The values of $x$ for which the inequality $\frac{8x^2+16x-51}{(2x-3)(x+4)} > 3$ holds,are

Find the set of all values of $x$ satisfying $\frac{x^4 - 4x^3 + 3x^2}{(x^2 - 4)(x^2 - 7x + 10)} \ge 0$.

If the set of all solutions of $|x^2 + x - 9| = |x| + |x^2 - 9|$ is $[\alpha, \beta] \cup [\gamma, \infty)$, then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to:

Solve the following inequality: $|x-1|+|x-2|+|x-3| \geq 6$

$A$ solution is to be kept between $68\,^{\circ} F$ and $77\,^{\circ} F$. What is the range in temperature in degree Celsius $(C)$ if the Celsius/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?

Let $a$ and $b$ be two positive real numbers such that $a+2b \leq 1$. Let $A_1$ and $A_2$ be respectively the areas of circles with radii $ab^3$ and $b^2$. Then,the maximum possible value of $\frac{A_1}{A_2}$ is