The set of real values of $x$ for which the inequality $|x-1|+|x+1| < 4$ holds true 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?

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

For $x$ and $y$ satisfying $|x|+|y|=|x-3|+|y-2|$,which of the following is correct?

Solve the following inequality: $\frac{|x-1|}{x+2} < 1$.

Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.