In addition to the deparse examples provided by haukex here, consider the OPed code and a slight modification. In the first, original version, constant folding (I think that's the correct phrase) makes the ternary go away and reduces the expression to a pure assignment (albeit a two-step one):

c:\@Work\Perl\monks>perl -wMstrict -MO=Deparse,-p -le
"my $a = 'a';
 my $b = 'b';
 1 ? $a = 2 : $b = 'x';
 print qq{a is $a};
 print qq{b is $b};
"
BEGIN { $^W = 1; }
BEGIN { $/ = "\n"; $\ = "\n"; }
use strict 'refs';
(my $a = 'a');
(my $b = 'b');
(($a = 2) = 'x');
print("a is $a");
print("b is $b");
-e syntax OK
[download]

Making the condition expression of the ternary non-constant preserves the ternary operator in all its LHS glory:

c:\@Work\Perl\monks>perl -wMstrict -MO=Deparse,-p -le
"my $a = 'a';
 my $b = 'b';
 my $p = 1;
 $p ? $a = 2 : $b = 'x';
 print qq{a is $a};
 print qq{b is $b};
"
BEGIN { $^W = 1; }
BEGIN { $/ = "\n"; $\ = "\n"; }
use strict 'refs';
(my $a = 'a');
(my $b = 'b');
(my $p = 1);
(($p ? ($a = 2) : $b) = 'x');
print("a is $a");
print("b is $b");
-e syntax OK
[download]

Please see O and B::Deparse.