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

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0$ is

The set of values of $x$ which satisfy $5x + 2 < 3x + 8$ and $\frac{x + 2}{x - 1} < 4$ is

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

$A$ container is filled with $1120 \text{ litres}$ of a solution containing $40 \%$ acid. How many litres of acid must be added so that the resulting mixture contains more than $40 \%$ but less than $50 \%$ water?

The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \geq 1$ is