Complete the following steps to prove the triangle inequality.(a) Let a and b be real numb...

Complete the following steps to prove the triangle inequality.

(a) Let a and b be real numbers. Which property in the summary box tells us that a ≤ |a| and b ≤ |b|?

(b) Add the two inequalities in part (a) to obtain a + b ≤ |a| + |b|.

(c) In a similar fashion, add the two inequalities −a ≤ |a| and −b ≤ |b| and deduce that −(a + b) ≤ |a| + |b|

(d) Why do the results in parts (b) and (c) imply that |a + b| ≤ |a| + |b|?

PROPERTY SUMMARY Properties of Absolute Value