Nested Absolute Value Equation involving Fractions: Guessing and Testing not Advised

Solution to nested absolute value equation abs(abs(x+2) - 3) = 34/11. What does nested mean in this mathematical context? It means absolute value bars contained within two absolute value bars.

Absolute value has been called idempotent which can mean the outer bars in absolute value expressions are unnecessary/superfluous in some cases.

For this particular problem idempotency does not apply and problem would be altered if one elected to ignore the outer bars.

My dark side created this problem to expose the guessing and testing mentality that is quite prevalent. You know the type who make comments like "I got the right answer in like 6 seconds man"

The main reason this happens is that problem composers frequently create problems with single digit integer answers. So I spent half a Saturday afternoon producing something that might confuse these guys!
A gentleman named Scott Bellware wrote about it back 2013 as it relates to computer science. He and Mark Burgess were using big words like instantiation which made me glad I stuck to math :)