If $x$ is real and satisfies $x + 2 > \sqrt{x + 4}$,then

Solve for $x$ the following inequality: $\frac{1}{|x|-3} \leq \frac{1}{2}$

The length of a rectangle is five times the breadth. If the minimum perimeter of the rectangle is $180 \ cm$,then:

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.

$A$ manufacturer has $600 \text{ litres}$ of a $12 \%$ solution of acid. How many litres of a $30 \%$ acid solution must be added to it so that the acid content in the resulting mixture will be more than $15 \%$ but less than $18 \%$?

The longest side of a triangle is $3$ times the shortest side and the third side is $2 \, cm$ shorter than the longest side. If the perimeter of the triangle is at least $61 \, cm$,find the minimum length of the shortest side. (in $, cm$)