1. The problem statement, all variables and given/known data Show that if |a-5| < 1/2 and |b-8| < 1/2 then |(a+b)-13| < 1. Hint: use the triangle inequality. 2. Relevant equations Triangle Inequality: |a+b| <= |a|+|b| 3. The attempt at a solution I really don't know how to use the triangle inequality so I was hoping someone could clear up for me exactly how it is used my book doesn't really make it clear it just states what it is which is what I have stated above. I understand why it is true, I just do not understand how you would use it in a problem. I plugged the first parts into it to get |(a-5)+(b-8)| <= |a-5| + |b-8| I'm not really sure how to simplify this though it should simplify to |a+b-13| but I can't get that everything is just canceling out for me.