The solution set of the inequation $\frac{x^{2}+6x-7}{|x+4|} < 0$ is

The least integral value $\alpha$ of $x$ such that $\frac{x - 5}{x^2 + 5x - 14} > 0$ satisfies:

Solve the following inequality: $\frac{|x+2|-x}{x} < 2$

In a manufacturing company,the cost and revenue functions of a product are given by $C(x) = 500 + \frac{5}{2}x$ and $R(x) = 3x$,where $x$ is the number of items produced and sold. How many items must be sold to realize no profit or loss? Is there any profit?

The number of points $P(x, y)$ with natural numbers as coordinates that lie inside the quadrilateral formed by the lines $2x + y = 2$,$x = 0$,$y = 0$,and $x + y = 5$ is

$A$ solution of $8 \%$ boric acid is to be diluted by adding a $2 \%$ boric acid solution to it. The resulting mixture is to be more than $4 \%$ but less than $6 \%$ boric acid. If we have $640$ litres of the $8 \%$ solution,how many litres of the $2 \%$ solution will have to be added?