Determine Which Property of Absolute Value Justifies the Statement $| x + y | \leq | x | + | y |$

question 459

Multiple Choice

Determine which property of absolute value justifies the statement.
- $| x + y | \leq | x | + | y |$

• A) Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers.
• B) Property 5: the sum of the absolute values of two numbers is less than or equal to the absolute value of their sum (the triangle inequality).
• C) Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of their absolute values (the triangle inequality).
• D) Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers.

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