document.write( "Question 255117: |2x-9|<11 \n" ); document.write( "

Algebra.Com's Answer #187422 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Learn the ways to rewrite absolute value inequalities\r\n" );
document.write( "without using absolute value bars:\r\n" );
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document.write( "\"\" refers to whatever is between the absolute value bars.\r\n" );
document.write( "\"\" refers to whatever POSITIVE* number is on the right side.\r\n" );
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document.write( "1.  can be rewritten without absolute value bars as \r\n" );
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document.write( "2.  can be rewritten without absolute value bars as \r\n" );
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document.write( "3.  can be rewritten without absolute value bars as , \r\n" );
document.write( "and the word \"\" must be included.\r\n" );
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document.write( "4,  can be rewritten without absolute value bars as ,\r\n" );
document.write( "and the word \"\" must be included.\r\n" );
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document.write( "Yours is case 1 but I thought I'd include the others so you could\r\n" );
document.write( "solve other inequalities you'll be studying.\r\n" );
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document.write( "The \"\" here is is what's between the absolute value bars,\r\n" );
document.write( "and that is \"\" and \"\" is . \r\n" );
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document.write( " can be rewritten without absolute value bars as \r\n" );
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document.write( "You solve \r\n" );
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document.write( "     -11 < 2x - 9 < 11\r\n" );
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document.write( "by getting x alone in the MIDDLE.  Begin by adding 9 to all\r\n" );
document.write( "three sides:\r\n" );
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document.write( "     -11 < 2x - 9 < 11\r\n" );
document.write( "      +9       +9   +9\r\n" );
document.write( "     -----------------\r\n" );
document.write( "      -2 < 2x     < 20\r\n" );
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document.write( "Then divide all three sides by 2 and\r\n" );
document.write( "since 2 is not a negative number the\r\n" );
document.write( "inequalities are not reversed.\r\n" );
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document.write( "     \r\n" );
document.write( "     \r\n" );
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document.write( "The graph of that solution is\r\n" );
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document.write( "---------o===========================================o--------\r\n" );
document.write( "-3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12 \r\n" );
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document.write( "and the interval notation for that is (-1, 10)\r\n" );
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document.write( "Edwin

\n" ); document.write( "* when N is not a positive number, there is no solution in
\n" ); document.write( "cases 1 and 2, and \"all real numbers\" in cases 3 and 4. \r
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