document.write( "Question 1209357: Let x, y, and z be nonzero real numbers. Find all possible values of
\n" ); document.write( "(x + y + z)/(|x| + |y| + |z|). \n" ); document.write( "
Algebra.Com's Answer #848628 by yurtman(42)\"\" \"About 
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**1. Consider the Sign Combinations**\r
\n" ); document.write( "\n" ); document.write( "* **All positive:** If x, y, and z are all positive, then:
\n" ); document.write( " (x + y + z) / (|x| + |y| + |z|) = (x + y + z) / (x + y + z) = 1\r
\n" ); document.write( "\n" ); document.write( "* **All negative:** If x, y, and z are all negative, then:
\n" ); document.write( " (x + y + z) / (|x| + |y| + |z|) = -(x + y + z) / (-(x + y + z)) = 1\r
\n" ); document.write( "\n" ); document.write( "* **Two positive, one negative:**
\n" ); document.write( " * Let's say x and y are positive, and z is negative:
\n" ); document.write( " (x + y + z) / (|x| + |y| + |z|) = (x + y - |z|) / (x + y + |z|)
\n" ); document.write( " This value will be between 0 and 1, depending on the relative magnitudes of x, y, and z.\r
\n" ); document.write( "\n" ); document.write( "* **Two negative, one positive:**
\n" ); document.write( " * Similar to the previous case, the value will be between -1 and 0.\r
\n" ); document.write( "\n" ); document.write( "* **One positive, two negative:**
\n" ); document.write( " * Similar to the previous cases, the value will be between -1 and 0.\r
\n" ); document.write( "\n" ); document.write( "**2. Determine the Possible Values**\r
\n" ); document.write( "\n" ); document.write( "* Based on the sign combinations, the possible values of (x + y + z) / (|x| + |y| + |z|) range from **-1 to 1**, inclusive.\r
\n" ); document.write( "\n" ); document.write( "**Therefore, the possible values of (x + y + z) / (|x| + |y| + |z|) are all real numbers in the interval [-1, 1].**
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