1. The problem statement, all variables and given/known data Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|. 2. Relevant equations The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and b. 3. The attempt at a solution |x-a| = |x-y+y-a| <= |x-y| + |y-a| I'm fairly certain this conversion/inequality is important because it contains three of the four elements from the problem ( |x-a|, |y-a|, and |x-y|). However, I am stuck on how to get E involved and determine an estimate for |x-y|.