Use the definition of the absolut value. You should consider 4 cases.
In solving an equation for e.g : 2x-7=9 we start by using some axioms or thoerem ,like adding or subtracting or multiplying both sides of the equation the equation will not change e.t.c
But in solving the equation : |x+2|+|x-3| =2 what axioms or definitions e.t.c can we use to start solving the equation??
The equation has no solution.
It is a very good example of showing that knowing the basics is the best way to do mathematics.
The expression is the distance from .
So look at that equation again.
The distance from to plus the distance from to equals .
Now draw a number line and mark off .
They are five units apart: .
So can there be an such that
I believe Plato wanted you to recognize that the sum of the distances from any point x on the number line to the points -2 and 3 is a minimum when:
and that sum is 5.
Look at the 2 solutions you obtained...do they violate your stated conditions?