Absolute Value

Absolute Value: Level 2 Challenges


x2=2x\Large \left| x-2 \right| = 2-x

Find the largest value of xx that satisfies the equation above.


x2x+1,\frac{\sqrt{x^2}}{|x|} + 1,

where xx is a non-zero real number.

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

1235n? \left| 123 - 5n \right| ?

If the solution set of the system of inequalities {a+1<3b1<10\begin{cases}\lvert a+1 \rvert < 3\\ \lvert b-1 \rvert <10 \end{cases} is x<a+b<y, x < a+b < y, then what are xx and y?y?

2=x2+x4\large 2=|x-2|+|x-4|

Find the solution set of the above equation.


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