Question 204633
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{{{abs(x-3) = 3-x}}}

Let's use the principle {{{abs(A)= abs(-A)}}}, to replace
the left side:

{{{abs(-(x-3)) = 3-x}}}

{{{abs(-x+3) = 3-x}}}

{{{abs(3-x) = 3-x}}}

Now we use the principle that {{{abs(A)=A}}} if and only if {{{M>=0}}}

Therefore {{{abs(3-x) = 3-x}}}

is true  if and only if  

{{{3-x>=0}}}

Subtract 3 from both sides:

{{{-x>=-3}}}

Multiply through by -1, which reverses the inequality:

{{{x<=3}}}

Or in interval notation {{{"("-infinity", 3]"}}}{{{",3]"}}}

The equation has infinitely many solutions.

Edwin</pre>