document.write( "Question 1207836: Show that \r
\n" ); document.write( "\n" ); document.write( "|a + b + c| <= |a| + |b| + |c|\r
\n" ); document.write( "\n" ); document.write( "for all real numbers a, b, and c. \r
\n" ); document.write( "\n" ); document.write( "Hint:\r
\n" ); document.write( "\n" ); document.write( "The left-hand side can be written
\n" ); document.write( "|a + (b + c)| . \r
\n" ); document.write( "\n" ); document.write( "Now use the triangle inequality. \n" ); document.write( "

Algebra.Com's Answer #845957 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Show that
\n" ); document.write( "|a + b + c| <= |a| + |b| + |c|
\n" ); document.write( "for all real numbers a, b, and c.
\n" ); document.write( "Hint:
\n" ); document.write( "The left-hand side can be written
\n" ); document.write( "|a + (b + c)| .
\n" ); document.write( "Now use the triangle inequality.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
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document.write( "              Step by step\r\n" );
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document.write( "(1)  Make grouping  |a + b + c| = |a + (b + c)|.\r\n" );
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document.write( "(2)  Apply the triangle inequality\r\n" );
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document.write( "         |a + (b + c)| <= |a| + |b + c|.\r\n" );
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document.write( "(3)  Apply the triangle inequality again to the second absolute value addend\r\n" );
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document.write( "         |a| + |b + c| <= |a| + |b| + |c|.\r\n" );
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document.write( "(4)  Combine the steps into the final conclusion\r\n" );
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document.write( "         |a + v + c| <= |a| + |b| + |c|.\r\n" );
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document.write( "At this point, the proof is fully completed.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanation.\r
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