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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.

Absolute Value: Level 2 Challenges


\[\Large \left| x-2 \right| = 2-x\]

Find the largest value of \(x\) that satisfies the equation above.


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

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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