I <3 conditionals

Question

You end up having a lot of very long, boring-looking conditionals in your code:

if flag == 1:

while have != needed:

if type == 7:

These can be transformed into their much more lovable <3 conditionals counterparts:

if abs(flag - 1) + 2 <3:

while 3 - abs(have - needed) <3:

if 2 + abs(type - 7) <3:

Task

Your task is to take a conditional and make it in terms of <3. The only spacing that matters is that there is none between < and 3.

Conditionals will be two expressions seperated by either ==, !=, >, <, >= or <=.
Expressions will only contain addition, subtraction, unary negation (-something), where there is one + or - before each variables or numbers (except the first which has nothing or - before it).
Numbers will be [0-9]+, and variables will be [a-z]+. If the answer needs to use |x| (The absolute value of x), use the abs() function. You may assume that all variables are integers, and all number constants in the input are < 1000.

The output does not need to be in it's simplest form. It does need to be a conditional like above, meaning that it is two expressions only, seperated by one conditional sign, but it can also use the abs function, enclosing a valid expression, and then it acts like a variable, in terms of validity.

If the input does not have an output for any value of a variable, output a condition that is always false, but still in terms of <3.

Part of the challenge is figuring out how to do it, but here are the steps for the have != needed above:

have != needed
have - needed != 0
abs(have - needed) > 0
-abs(have - needed) < 0
3 - abs(have - needed) <3

Scoring

This is code-golf, so the shortest valid code, in bytes, wins.

Test cases

(Note, these outputs aren't the only outputs, but I tried to simplify them.)

flag == 1
abs(flag - 1) + 2 <3

have != needed
3 - abs(have - needed) <3

type == 7
2 + abs(type - 7) <3

x > y
3 - x + y <3

x + 5 < -y
x + 8 + y <3

x + 6 <= y
x + 8 - y <3

-x >= y + 3
x + y + 5 <3

x < x
3 <3
# Unsimplified; both would be valid outputs.
x - x + 3 <3

Answer 1

Retina, 95 bytes

<=
<1+
>=
>-1+
(.*)(.=)(.*)
$2abs($1-($3))
==
2+
!=
3-
(.*)>(.*)
$2<$1
(.*)<(.*)
$1-($2)+3
$
<3

Try it online!

A rather naïve solution, but I haven't been able to find any improvements.

This is just a series of replacements:

<=
<1+
>=
>-1+

Get rid of "or equal to" comparisons by replacing x <= y with x < 1 + y, and x >= y with x > -1 + y.

(.*)(.=)(.*)
$2abs($1-($3))

Replace x == y with ==abs(x - y), and x != y with !=abs(x - y).

==
2+
!=
3-

Replace == with 2+ and != with 3-, so that the overall replacements become x == y → 2 + abs(x - y) and x != y → 3 - abs(x - y).

(.*)>(.*)
$2<$1

Normalize the direction of the remaining inequalities, replacing x > y with y < x.

(.*)<(.*)
$1-($2)+3

Replace x < y with x - y + 3.

$
<3

Append a heart to the end of the string.