A proof of the triangle inequality Give the reason justifying each of the numbered steps in the following proof of the triangle inequality. |a + b|2 = (a + b)² = a? + 2ab + b² (1) < a² + 2|a||b| + b² = |a|² + 2|a||b| + |b|2 = (la| + \b[)? la + b| < |a| + |b| (2) (3) (4)

Search the menus (Alt+/) 100% Normal text Calibri + BI U A 14 ... 2 II 3 | 4 |I 5 6 EUA Part B: Solving & Graphi... 2) For each of the following problems, write the inequality that is graphed on the number line. [(Answers should describe the inequality in terms of x, and use equality or inequality symbols, such as =, , 2, or s.] 3 of 4 Inequality Graph Inequality statement a. +++ 8 -7 -6 -5 4 3 -2 -1 0 1 2 3 4 5 6 7 b. ++++ 0 1 2 3 4 -8 -7 -6 -5 4 -3 -2 -1 5 C. +++ -8 -7 -6 -5 4 -3 -2 -1 0 1 2 3 4 5 6 7 8 2)

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