document.write( "Question 447471: Solve the absolute value inequality. Write the solution set using interval notation
\n" ); document.write( "|b + 4| - 7 > 11
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #308048 by Edwin McCravy(20054)\"\" \"About 
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( "
\n" );