document.write( "Question 564156: |2- $\"5%2F7\"$ x|≤3
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Algebra.Com's Answer #365265 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "    |2-x|≤3  To remove absolute value bars write this:\r\n" );
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document.write( " -3 < 2-x < 3   Solve for x in the middle:\r\n" );
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document.write( "Clear of fractions by multiplying through by 7\r\n" );
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document.write( "Get rid of the 42 in the middle by adding -42 to all three sides:\r\n" );
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document.write( "-21 ≤ 42-7x ≤  21\r\n" );
document.write( "-42  -42      -42\r\n" );
document.write( "-63 ≤   -7x ≤ -21\r\n" );
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document.write( "We must divide through by -7, but when we divide through\r\n" );
document.write( "by a negative number we must reverse the inequalities:\r\n" );
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document.write( " ≥  ≥ \r\n" );
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document.write( "9 ≥ x ≥ 3\r\n" );
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document.write( "This is equivalent to\r\n" );
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document.write( "3 ≤ x ≤ 9  it is usually preferred to write it with ≤ rather than ≥:\r\n" );
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document.write( "The solution is   3 ≤ x ≤ 9\r\n" );
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document.write( "The graph of the solution set is this:\r\n" );
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document.write( "--------⚫====================⚫---------  \r\n" );
document.write( "        3                    9  \r\n" );
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document.write( "Since we have ≤ and not < we include the endpoints of the interval,\r\n" );
document.write( "and use darkened circles at the endpoints to indicate this.\r\n" );
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document.write( "The interval notation for the solution set is this:\r\n" );
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document.write( "            [3,9]\r\n" );
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document.write( "and we use brackets [ ] instead of parentheses ( ) to indicate that\r\n" );
document.write( "the endpoints are both included in the solution set.\r\n" );
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document.write( "Edwin

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