For an equation, you can add the same number to both sides, subtract the same from both, or multiply or divide by the same on both.
How are these rules different for an inequality?
You can always add the same number to both sides of an inequality or subtract the same number from both sides. That's the same as with an equation.
If you multiply or divide by a positive number, that's also the same as with an equation. As long as you use the same number on both sides, it's fine.
The BIG difference is: if you multiply or divide both sides of an inequality by a NEGATIVE number, the direction of the inequality reverses. For example,
7 > 2
The inequality is open to the left. Now, multiply both sides by (–2):
–14 < –4
This process reversed the direction of the inequality: it now is open to the right.