document.write( "Question 150360: |-3x-5|>=2\r
\n" ); document.write( "\n" ); document.write( "The answer should have form b < x < c
\n" ); document.write( "or the form x < b or x > c
\n" ); document.write( "Is all my paper says to do.
\n" ); document.write( "I dont understand HOW they want me to put it in that form and do the problem.
\n" ); document.write( "The topic on the paper says, Absolute Value Inequalities.\r
\n" ); document.write( "\n" ); document.write( "I would greatly appreciate it if someone coul dhelp me figur eout how to do this, and show me how they had done it so i can learn how to do it myself.\r
\n" ); document.write( "\n" ); document.write( "Thanks,
\n" ); document.write( "KKG.
\n" ); document.write( "

Algebra.Com's Answer #110297 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
 \r\n" );
document.write( "\r\n" );
document.write( "\"%28-3x-5%29%3E=2\"\r\n" );
document.write( "\r\n" );
document.write( "--------------------------------------------\r\n" );
document.write( "Learn rules for removing absolute values from\r\n" );
document.write( "inequalities of these forms:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Rule 1:\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "      \r\n" );
document.write( "\"abs%28EXPRESSION%29%3CN\", \"abs%28EXPRESSION%29%3C=N\" (where N is not negative)\r\n" );
document.write( "\r\n" );
document.write( "Write as \r\n" );
document.write( "\r\n" );
document.write( "\"-N+%3C+EXPRESSION+%3C+N\", \"-N+%3C=+EXPRESSION+%3C=+N\", respectively.\r\n" );
document.write( "\r\n" );
document.write( "then solve. [If N is negative, there is no solution,\r\n" );
document.write( "and solution set = Ø)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------------------\r\n" );
document.write( "------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Rule 2:\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "\"abs%28EXPRESSION%29%3EN\", \"abs%28EXPRESSION%29%3E=N\" (where N is not negative)\r\n" );
document.write( "\r\n" );
document.write( "Write as \r\n" );
document.write( "\r\n" );
document.write( "\"EXPRESSION+%3C+-N\"\"OR\"\"EXPRESSION+%3E+N\", \"EXPRESSION+%3C=+-N\"\"OR\"\"EXPRESSION+%3E=+N\"\r\n" );
document.write( "respectively.\r\n" );
document.write( "\r\n" );
document.write( "Then solve each part.  (If N is negative, solution set is \r\n" );
document.write( "\"all real numbers\".)\r\n" );
document.write( "------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "You need Rule 2.  I gave you Rule 1 also because you\r\n" );
document.write( "will need it for other problems:\r\n" );
document.write( "\r\n" );
document.write( "\"abs%28-3x-5%29%3E=2\"\r\n" );
document.write( "\r\n" );
document.write( "\"EXPRESSION+=+-3x-5\"\r\n" );
document.write( "\r\n" );
document.write( "\"N=2\"\r\n" );
document.write( "\r\n" );
document.write( "So write:\r\n" );
document.write( "\r\n" );
document.write( "\"-3x-5+%3C=+-2\"\"OR\"\"-3x-5+%3E=+2\"\r\n" );
document.write( "\r\n" );
document.write( "Solve each part:\r\n" );
document.write( "\r\n" );
document.write( "Add 5 to both sides of both parts:\r\n" );
document.write( "\r\n" );
document.write( "\"-3x+%3C=+3\"\"OR\"\"-3x+%3E=+7\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides of both parts by \"-3\",\r\n" );
document.write( "Notice that dividing an inequality by a NEGATIVE\r\n" );
document.write( "NUMBER reverses the inequality sign:\r\n" );
document.write( "\r\n" );
document.write( "\"%28-3x%29%2F%28-3%29+%3E=+3%2F%28-3%29\"\"OR\"\"%28-3x%29%2F%28-3%29+%3C=+7%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "\"x+%3E=+-1\"\"OR\"\"x+%3C=+-7%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "So we shade the number line:\r\n" );
document.write( "\r\n" );
document.write( "1. to the right of -1\r\n" );
document.write( "and\r\n" );
document.write( "2. to the left of \"-7%2F3\", which is the same as \"-2\"\"1%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<=======@-----------@==================>\r\n" );
document.write( " -3       -2       -1        0        1            \r\n" );
document.write( "\r\n" );
document.write( "The circles should be darkened since the inequalities\r\n" );
document.write( "are all underlined:\r\n" );
document.write( "\r\n" );
document.write( "Solution in interval notation is \r\n" );
document.write( "\r\n" );
document.write( "(\"-infinity\",\"-7%2F3\"] U [\"-1\",\"infinity\")\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "
\n" ); document.write( "
\n" );