10. When you add the same number to both sides of an inequality, is the inequality still true? Explain how you know your statement holds for subtracting the same number?

The inequality is still true! If you add a number, say 5 to both sides of the following inequality, does anything change?

3 < 6

3 + 5 < 6 + 5

8 < 11

The inequality is still true. We know the statement holds for subtracting the same number because, in a way, addition and subtraction are pretty much the same operation. If I subtract 5 from both sides, I can think of it like "I add negative 5 to both sides" or something along those lines. It's kind of backwards thinking.