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

question 544

Multiple Choice

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

• A) Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers.
• B) 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).
• C) Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers.
• D) 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).

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Definitions:

Benzoic Acid

A simple aromatic carboxylic acid with the formula C6H5COOH, used widely as a food preservative.

Methylamine

A simple organic compound consisting of a methyl group linked to an amine group, commonly used in organic synthesis.

Compound

A substance formed by the chemical combination of two or more elements in definite proportions and structure.

Aniline

An organic compound, specifically an amine derived from benzene, widely used in dyes and polymers.