document.write( "Question 1199343: Find a and b.\r
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document.write( "If -3 < x < 0, then a < 1/(x + 4) < b \n" );
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Algebra.Com's Answer #833190 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Add four to all sides of the 1st inequality \n" ); document.write( "-3 < x < 0 \n" ); document.write( "-3+4 < x+4 < 0+4 \n" ); document.write( "1 < x+4 < 4 \n" ); document.write( "The inequality signs stay the same for now.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Then apply the reciprocal to all three sides. \n" ); document.write( "This flips the direction of the inequality signs. \n" ); document.write( "It's like saying how 2 > 1/3 flips to 1/2 < 3.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So, \n" ); document.write( "1 < x+4 < 4 \n" ); document.write( "1/1 > 1/(x+4) > 1/4 \n" ); document.write( "1 > 1/(x+4) > 1/4\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now let's go from the form p > q > r to r < q < p \n" ); document.write( "1 > 1/(x+4) > 1/4 \n" ); document.write( "1/4 < 1/(x+4) < 1 \n" ); document.write( "In other words, swap the 1st and last sides so that the \"greater than\" signs become \"less than\" signs.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Compare that to the form \n" ); document.write( "a < 1/(x+4) < b \n" ); document.write( "to find that \n" ); document.write( "a = 1/4 \n" ); document.write( "b = 1 \n" ); document.write( "which are the final answers. \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |