just a sidenote: (of course using eval in your context is extremely not secure, so you might want to change your code logic to include specific expressions: like if you want them to evaluate '5 < 7' then take the inputs each one alone and test them one by one to construct the expression, or something like that)
anyway

if (eval($expression)) {
  $output = $true;
} else {
  $output = $false;
}
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using eval() will not tell you what went wrong, you probably want to use the eval-BLOCK to catch errors and warnings in $@.

eval { $expression };
$output = defined $@ ? $false : $true;
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