document.write( "Question 109466: what is solution for
\n" ); document.write( " a)|x|>-2
\n" ); document.write( " b)|x|-2=-3 \n" ); document.write( "

Algebra.Com's Answer #79806 by jim_thompson5910(35256) $\"\"$ $\"About$

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a)\r
\n" ); document.write( "\n" ); document.write( " $\"abs%28x%29%3E-2\"$ Start with the given inequality\r
\n" ); document.write( "\n" ); document.write( "Since the absolute value of any number is always positive, this means $\"abs%28x%29%3E0\"$ . So this means the left side will always be greater than -2. So the solution set is

. Basically x can be any number.\r
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\n" ); document.write( "\n" ); document.write( " $\"abs%28x%29-2=-3\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"abs%28x%29=-1\"$ Add 2 to both sides.\r
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\n" ); document.write( "\n" ); document.write( "Since the expression $\"abs%28x%29=-1\"$ is never true (note: remember, the absolute value of any number is always positive), there are no solutions to $\"abs%28x%29=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Also, notice if we graph $\"y=abs%28x%29-2\"$ and $\"y=-3\"$ (just set each side equal to y and graph), we get:\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28500%2C500%2C-10%2C10%2C-10%2C10%2Cabs%28x%29-2%2C-3%29\"$ Graph of $\"y=abs%28x%29-2\"$ (red) and $\"y=-3\"$ (green)\r
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\n" ); document.write( "\n" ); document.write( "and we can see that the two graphs never intersect. So there are no solutions.
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