document.write( "Question 447471: Solve the absolute value inequality. Write the solution set using interval notation
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document.write( "|b + 4| - 7 > 11
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Algebra.Com's Answer #308048 by Edwin McCravy(20054)![]() ![]() You can put this solution on YOUR website! Exponents/447471 (2011-05-10 08:40:47): Solve the absolute value inequality. Write the solution set using interval notation\r \n" ); document.write( "\n" ); document.write( "|b + 4| - 7 > 11 \n" ); document.write( " \r\n" ); document.write( "Get the absolute value term by itself by adding 7 to both sides:\r\n" ); document.write( "\r\n" ); document.write( " |b + 4| > 18\r\n" ); document.write( "\r\n" ); document.write( "There are four rules for removing absolute value bars in\r\n" ); document.write( "absolute value inequalities:\r\n" ); document.write( "\r\n" ); document.write( "If A is positive:\r\n" ); document.write( "\r\n" ); document.write( "1. |EXPRESSION| < A becomes \r\n" ); document.write( "\r\n" ); document.write( "-A < EXPRESSION < A\r\n" ); document.write( "\r\n" ); document.write( "2. |EXPRESSION| ≦ A becomes \r\n" ); document.write( "\r\n" ); document.write( "-A ≦ EXPRESSION ≦ A\r\n" ); document.write( "\r\n" ); document.write( "3. |EXPRESSION| > A becomes\r\n" ); document.write( "\r\n" ); document.write( "EXPRESSION < -A OR EXPRESSION > A \r\n" ); document.write( "\r\n" ); document.write( "4. |EXPRESSION| ≧ A becomes\r\n" ); document.write( "\r\n" ); document.write( "EXPRESSION ≦ -A OR EXPRESSION ≧ A\r\n" ); document.write( "\r\n" ); document.write( "-----------------------------------------\r\n" ); document.write( "\r\n" ); document.write( " |b + 4| > 18\r\n" ); document.write( "\r\n" ); document.write( "is rule 3 above where EXPRESSION = b + 4 and A = 4\r\n" ); document.write( "\r\n" ); document.write( " |b + 4| > 18 becomes\r\n" ); document.write( "\r\n" ); document.write( "b + 4 < -18 OR b + 4 > 18\r\n" ); document.write( "\r\n" ); document.write( "Solve each for b:\r\n" ); document.write( "\r\n" ); document.write( " b < -22 OR b > 14 \r\n" ); document.write( "\r\n" ); document.write( "Draw the graph on a number line:\r\n" ); document.write( "\r\n" ); document.write( "<==============o-----------------------o===============>\r\n" ); document.write( " -22 14 \r\n" ); document.write( "\r\n" ); document.write( "Then the interval notation for this is an abbreviation \r\n" ); document.write( "for this graph\r\n" ); document.write( "\r\n" ); document.write( " (-∞,-22) U (14,∞)\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |