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PROVE: Triangle Inequality We prove Property 5 of abso- lute values, the Triangle Inequality: |x + y < |x| + y| (a) Verify that the Triangle Inequality holds for x = 2 and y = 3, for x = -2 and y = -3, and for x = -2 and y = 3. (b) Prove that the Triangle Inequality is true for all real num- bers x and y. [Hint: Take cases.]

PROVE: Triangle Inequality We prove Property 5 of abso- lute values, the Triangle Inequality: |x + y < |x| + y| (a) Verify that the Triangle Inequality holds for x = 2 and y = 3, for x = -2 and y = -3, and for x = -2 and y = 3. (b) Prove that the Triangle Inequality is true for all real num- bers x and y. [Hint: Take cases.]

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PROVE: Triangle Inequality We prove Property 5 of abso- lute values, the Triangle Inequality: |x + y < |x| + y| (a) Verify that the Triangle Inequality holds for x = 2 and y = 3, for x = -2 and y = -3, and for x = -2 and y = 3. (b) Prove that the Triangle Inequality is true for all real num- bers x and y. [Hint: Take cases.]
Transcribed Image Text:PROVE: Triangle Inequality We prove Property 5 of abso- lute values, the Triangle Inequality: |x + y < |x| + y| (a) Verify that the Triangle Inequality holds for x = 2 and y = 3, for x = -2 and y = -3, and for x = -2 and y = 3. (b) Prove that the Triangle Inequality is true for all real num- bers x and y. [Hint: Take cases.]
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