document.write( "Question 978838: how to prove x ≤ |x| \n" ); document.write( "

Algebra.Com's Answer #600243 by Fombitz(32388) $\"\"$ $\"About$

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If $\"x%3E=0\"$ then $\"abs%28x%29=x\"$ so then,
\n" ); document.write( " $\"x%3C=x\"$
\n" ); document.write( " $\"x-x%3C=0\"$
\n" ); document.write( " $\"0%3C=0\"$
\n" ); document.write( "True because $\"0=0\"$ .
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\n" ); document.write( "If $\"x%3C0\"$ then $\"abs%28x%29=-x\"$ so then,
\n" ); document.write( " $\"x%3C=-x\"$
\n" ); document.write( " $\"2x%3C=0\"$
\n" ); document.write( "However since $\"x%3C0\"$ , then $\"2x%3C0\"$ so this statement is also true since
\n" ); document.write( " $\"2x%3C0\"$
\n" ); document.write( "So you've proved it when $\"x%3E=0\"$ and when $\"x%3C0\"$ , so the statement holds for all $\"x\"$ . \n" ); document.write( "

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