![\"\"](\"/images/stars/stars-13.gif\")
You can put this solution on YOUR website!
\r\n" );
document.write( "He only did the first inequality and ignored the second because he took \"or\"\r\n" );
document.write( "to mean that you are to solve either the first inequality or the second\r\n" );
document.write( "inequality, whichever you choose, and you do not need to even look at the\r\n" );
document.write( "other one.\r\n" );
document.write( "\r\n" );
document.write( "But that's the wrong way to take \"or\".\r\n" );
document.write( "\r\n" );
document.write( "5x - 6 < -16 or -4x ≤ -20\r\n" );
document.write( "\r\n" );
document.write( "If he's listening, the problem is to give the solution set for this:\r\n" );
document.write( "\r\n" );
document.write( "{x | 5x-6 < -16} U {x | -4x ≤ -20}\r\n" );
document.write( "\r\n" );
document.write( "The U means the union of the two sets.\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Solve the first inequality:\r\n" );
document.write( "\r\n" );
document.write( "5x - 6 < -16\r\n" );
document.write( "\r\n" );
document.write( "Add +6 to both sides:\r\n" );
document.write( "\r\n" );
document.write( " 5x < -10\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 5, which does NOT flip the inequality, because we\r\n" );
document.write( "are dividing by a POSITIVE.\r\n" );
document.write( "\r\n" );
document.write( " x < -10 <--first inequality simplified\r\n" );
document.write( "\r\n" );
document.write( "******************************************************************\r\n" );
document.write( "\r\n" );
document.write( "Now solve the second inequality\r\n" );
document.write( "\r\n" );
document.write( " -4x ≤ -20\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by -4, which DOES flips the inequality, because we\r\n" );
document.write( "are dividing by a NEGATIVE.\r\n" );
document.write( "\r\n" );
document.write( " x ≥ 5 <--second inequality simplified\r\n" );
document.write( "\r\n" );
document.write( "******************************************************************\r\n" );
document.write( "\r\n" );
document.write( "We plot the first one:\r\n" );
document.write( "\r\n" );
document.write( " x < -10 <--first inequality simplified.\r\n" );
document.write( "\r\n" );
document.write( "Plot it on a number line by shading everything left of -10, and we put an open\r\n" );
document.write( "circle at -10 because the inequality is < and not ≤.\r\n" );
document.write( "\r\n" );
document.write( "-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8\r\n" );
document.write( "<=========o------------------------------------------------------------------------ \r\n" );
document.write( "\r\n" );
document.write( "Now we plot the second one:\r\n" );
document.write( "\r\n" );
document.write( " x ≥ 5 <--second inequality simplified.\r\n" );
document.write( "\r\n" );
document.write( "Plot it on a number line by shading the 5 and everything RIGHT of 5, and we put a\r\n" );
document.write( "closed circle at 5 because the inequality is ≥ and not >.\r\n" );
document.write( "\r\n" );
document.write( "-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8\r\n" );
document.write( "----------------------------------------------------------------------☻===========>\r\n" );
document.write( "\r\n" );
document.write( "Now we combine the two number lines because what is shaded must be in the solution\r\n" );
document.write( "for the first inequality OR the second inequality.\r\n" );
document.write( "\r\n" );
document.write( "-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8\r\n" );
document.write( "<=========o-----------------------------------------------------------☻===========> \r\n" );
document.write( "\r\n" );
document.write( "Then we write the solution set in interval notation, which is an abbreviation for\r\n" );
document.write( "the above number line:\r\n" );
document.write( "\r\n" );
document.write( "(-∞,-10) U [5,∞) <--answer\r\n" );
document.write( "\r\n" );
document.write( "Edwin