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3(7 - m( < 4(2 - m)
\n" ); document.write( "Solving inequalities is nearly exactly the same as solving equations. (The only exception is: If you multiply or divide both sides of an inequality by any negative number, then the inequality symbol must be reversed.)
\n" ); document.write( "First we simplify each side:
\n" ); document.write( "21 - 3m < 8 - 4m
\n" ); document.write( "Second we get the variable on just one side. To avoid having to remember the exception I described above, it is helpful to gather the variable terms on the side with the larger coefficient. Since -3 is larger than -4, I am going to get the variable on the left side (where the -3m is) by adding 4m to each side:
\n" ); document.write( "21 + m < 8
\n" ); document.write( "Last of all we isolate the variable. In this equation we want the 21 to go away. So we'll subtract 21 from each side:
\n" ); document.write( "m < -13
\n" ); document.write( "which is the solution.
\n" ); document.write( "If we don't end up with a positive coefficient for the variable, then the last step will be to multiply or divide each side by a negative number. For example, with your problem, after we simplify
\n" ); document.write( "21 - 3m < 8 - 4m
\n" ); document.write( "we could get the variable on just one side by adding 3m to each side:
\n" ); document.write( "21 < 8 - m
\n" ); document.write( "Then subtract 8 from each side:
\n" ); document.write( "13 < -m
\n" ); document.write( "And last of all we divide both sides by -1 (which means we need to remember the exception):
\n" ); document.write( "-13 > m
\n" ); document.write( "(Note how the inequality symbol has been reversed!) This solution is the same as the one we found earlier. They both say \"m is less than -13\". (Always read inequalities from where the variable is. So for \"-13 > m\" we should read it from right to left because the variable in on the right. And from right to left \"-13 > m\" says \"m is less than -13\".) \n" ); document.write( "