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## Absolute Value

Absolute value is a mathematician's way of judging numbers by their magnitude rather than their positive/negative value. It is the distance of the number from 0 on a number line.

# Level 2

$\Large \left| x-2 \right| = 2-x$

Find the largest value of $$x$$ that satisfies the equation above.

Evaluate

$\frac{\sqrt{x^2}}{|x|} + 1,$

where $$x$$ is a non-zero real number.

If $$n$$ is an integer, then what is the least possible value of

$\left| 123 - 5n \right| ?$

If the solution set of the system of inequalities $\begin{cases}\lvert a+1 \rvert < 3\\ \lvert b-1 \rvert <10 \end{cases}$ is $$x < a+b < y,$$ then what are $$x$$ and $$y?$$

$\large 2=|x-2|+|x-4|$

Find the solution set of the above equation.

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