Which of the following inequalities is always true for any real number 'x' and 'y'?  Pick one.
A) |x-y| < |x| +|y| B) |x + y| > |y| + |x| C) |x + y| <= |x| + |y| D) |x - y| <= |x| - |y| E) |x - y| > |x| - |y|
The answer is (C). One of the fundamental properties of absolute value, which is subadditivity, essentially means that evaluating the function for the sum of two elements (numbers) always returns something less than or equal to the sum of the function's values at each element; therefore, |x + y| &lt;= |x| + |y|
<result>C</result>
Which of the following inequalities is always true for any real number 'x' and 'y'?