terminallychill 2 years ago -1 ≤ a − 3 ≤ 2 solve compound inequality, help.

1. tcarroll010

With inequalities, you can add or subtract numbers to all sides and retain the direction of the sign. So, find a number such that if you add it to "a - 3" you end up with "a". Take that number and add it to all 3 expressions.

2. terminallychill

I'm still really confused...

3. tcarroll010

You are looking for (a - 3) + x = a That is the same as: a + (x - 3) = a So, you are looking for where x - 3 = 0. What is "x"? You add whatever "x" is to all 3 expression and you get "a" all by itself.

4. terminallychill

5. tcarroll010

Yes, to the left, center, and right-side expressions.

6. tcarroll010

So, for the left-side, you get 3 - 1 because that is adding 3 to the left.

7. tcarroll010

When you add 3 to the center expression, you get (a - 3) + 3 = a + (3 - 3) = a + 0 = a, which is what you want. The right-side expression, before simplifying, is 2 + 3.

8. terminallychill

I'm lost again...ha :c

9. tcarroll010

For the left, you have 3 - 1. What is that?