document.write( "Question 986111: Solve and check the inequality, if possible.\r
\n" ); document.write( "\n" ); document.write( "|4m + 8| < 12 \n" ); document.write( "

Algebra.Com's Answer #606847 by MathLover1(20850) $\"\"$ $\"About$

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$\"abs%284m+%2B+8%29+%3C+12\"$ ...............since $\"abs%284m+%2B+8%29=sqrt%28%284m+%2B+8%29%5E2%29\"$ , we will have\r
\n" ); document.write( "\n" ); document.write( " $\"4m+%2B+8%3C+12\"$ and $\"-%284m+%2B+8%29%3C+12\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"4m+%2B+8%3C+12\"$ => $\"4m+%3C+12-8\"$ => $\"4m+%3C+4\"$ => $\"highlight%28m+%3C+1%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"-%284m+%2B+8%29%3C+12\"$ => $\"-4m+-+8%3C+12\"$ => $\"-12+-+8%3C+4m\"$ => $\"-20%3C+4m\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"-20%2F4%3C+m\"$ => $\"-5%3C+m\"$ or $\"highlight%28m%3E-5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "interval: $\"-5%3Cm%3C1\"$ \r
\n" ); document.write( "\n" ); document.write( "so,solution set is: $\"-4\"$ , $\"-3\"$ , $\"-2\"$ , $\"-1\"$ ,and $\"0\"$ \r
\n" ); document.write( "\n" ); document.write( "check:
\n" ); document.write( " $\"m=-4\"$
\n" ); document.write( " $\"abs%284%28-4%29+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-16+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-8%29+%3C+12\"$
\n" ); document.write( " $\"8+%3C+12\"$ .............true\r
\n" ); document.write( "\n" ); document.write( " $\"m=-3\"$
\n" ); document.write( " $\"abs%284%28-3%29+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-12+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-4%29+%3C+12\"$
\n" ); document.write( " $\"4+%3C+12\"$ .............true\r
\n" ); document.write( "\n" ); document.write( " $\"m=-2\"$
\n" ); document.write( " $\"abs%284%28-2%29+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-8+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%280%29+%3C+12\"$
\n" ); document.write( " $\"0+%3C+12\"$ .............true\r
\n" ); document.write( "\n" ); document.write( " $\"m=-1\"$
\n" ); document.write( " $\"abs%284%28-1%29+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%28-4+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%284%29+%3C+12\"$
\n" ); document.write( " $\"4+%3C+12\"$ .............true\r
\n" ); document.write( "\n" ); document.write( " $\"m=0\"$
\n" ); document.write( " $\"abs%284%280%29+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%280+%2B+8%29+%3C+12\"$
\n" ); document.write( " $\"abs%288%29+%3C+12\"$
\n" ); document.write( " $\"8+%3C+12\"$ .............true\r
\n" ); document.write( "\n" ); document.write( " $\"number_line%28+600%2C+-10%2C+10%2C+-5%2C+1+%29\"$
\n" ); document.write( " \n" ); document.write( "

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