A couple of things to note first:

(1) The "/" before the "=" is usually incorrect. By default, Perl uses forward-slashes as "pattern terminators" to match a pattern, like so:

Code:

if (/abc/) { <do-something> }

So a forward-slash inside the pattern will not work by default.
You could make it work, however, if you use non-default pattern terminators with the "m" (match) operator, like so:

Code:

if (m|abc/def|) { <do-something> }

Many other pattern terminators and even "pairs" are allowed: "[]", "{}", "()", "!!" etc.

(2) Note that the forward-slash was not present inside the pattern in the original solution. So, if your intention was to escape the "=", then the correct character is the back-slash "\". And even then, the "=" does not need to be escaped in Perl. It does not hold any special meaning.
So, now the regex is reduced to:

Code:

.+-=^\w+

(3) Next, notice the caret ("^"). It is a start-of-line anchor. It does not match any character. It matches a position: the "start of pattern". Hence it is always used at the start of the pattern. If you use it within the pattern, it will not match anything.
So, now the regex is reduced to:

Code:

^.+-=\w+

(4) Now if you take a step back and look at the original regex:

Code:

/^\w+=.+-/
/              => left pattern terminator
^              => beginning of pattern
\w+            => a word (by definition, a "word" does not have hyphens in Perl)
=              => followed by the "=" character
.+             => 1 or more occurrences of any character
-              => followed by a hyphen character
/              => right pattern terminator

In the original regex, we stop the moment we reach a "-" on the right hand side. We found what we wanted, so we take the relevant action.

But when you switch the patterns around the "=" character, that may not be true. So you put something after the "-" character on the left hand side, like so:

Code:

^.+-\w+=\w+

(5) Finally, you want to ensure that the word on the right hand side does not have any hyphens. The regex above matches a "word" on the right hand side, but if that "word" is followed by a hypen, it will still match it.

To ensure that you have a word without any hyphens on the right hand side till the end of the string, you put a "end of pattern" anchor: "$".
It is the counterpart of the "start of pattern" anchor: "^".
So now the regex becomes:

Code:

^.+-\w+=\w+$

And it should work with your data:

Code:

$
$ echo "a-levels=eilevelz" | perl -lne 'if (/^.+-\w+=\w+$/){print "matched"} else {print "unmatched"}'
matched
$
$ echo "alevels=ei-levelz" | perl -lne 'if (/^.+-\w+=\w+$/){print "matched"} else {print "unmatched"}'
unmatched
$
$ echo "a-levels=ei-levelz" | perl -lne 'if (/^.+-\w+=\w+$/){print "matched"} else {print "unmatched"}'
unmatched
$
$ echo "alevels=eilevelz" | perl -lne 'if (/^.+-\w+=\w+$/){print "matched"} else {print "unmatched"}'
unmatched
$
$

You could, alternatively use the regex

Code:

/^\w+-\w+=\w+$/