document.write( "Question 1207835: Show that for all real numbers a and b, we have \r
\n" ); document.write( "\n" ); document.write( "|a| - |b| <= |a - b|\r
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\n" ); document.write( "\n" ); document.write( "Hint:\r
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\n" ); document.write( "\n" ); document.write( "Beginning with the identity a = (a - b) + b, take the absolute value of each side and then use the triangle inequality. \n" ); document.write( "

Algebra.Com's Answer #845960 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Show that for all real numbers a and b, we have
\n" ); document.write( "|a| - |b| <= |a - b|\r
\n" ); document.write( "\n" ); document.write( "Hint:\r
\n" ); document.write( "\n" ); document.write( "Beginning with the identity a = (a - b) + b, take the absolute value of each side
\n" ); document.write( "and then use the triangle inequality.
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\n" ); document.write( "\n" ); document.write( "I will strictly follow the given instructions.\r
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document.write( "             Step by step\r\n" );
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document.write( "(1)  Start with the identity a = (a - b) + b.\r\n" );
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document.write( "(2)  Take absolute values\r\n" );
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document.write( "         |a| = |(a-b) + b|.\r\n" );
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document.write( "(3)  Apply the triangle inequality\r\n" );
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document.write( "          |a| = |(a-b) + b| <= |a-b| + |b|.\r\n" );
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document.write( "     So, you have \r\n" );
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document.write( "          |a| <= |a-b| + |b|.\r\n" );
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document.write( "(4)  In the last equality, subtract |b| from both sides\r\n" );
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document.write( "     (it is the same as transfer term |b| from right to left).  You will get\r\n" );
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document.write( "          |a| - |b| <= |a-b|.\r\n" );
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document.write( "     It is precisely what they want you prove.\r\n" );
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document.write( "At this point, the proof is complete.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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