Question 73249
{{{-2(n-8)>-n+4}}}
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Do the distributive multiplication on the left side to get:
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{{{-2n + 8> -n + 4}}}
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Subtract 8 from both sides to eliminate the -8 on the left side.  After the subtraction
the inequality is:
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{{{-2n > -n - 4}}}
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Add an n to both sides to eliminate the -n on the right side. After this addition, the inequality
becomes:
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{{{ -n > -4}}}
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But we need to solve this inequality for +n, so multiply both sides by minus 1.  However,
an IMPORTANT rule of inequalities is that whenever you multiply or divide both sides
by a negative number, you must reverse the direction of the inequality sign.  [You can
add or subtract negative numbers to both sides without this change of direction, but multiplying
and dividing do require the change of direction.]
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Anyhow, after multiplying both sides by -1 (and reversing the direction) we get:
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{{{n < 4}}}
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So n must be smaller than +4 for the inequality to hold.  
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Let's do a spot check.  Suppose we set n = 0.  That certainly meets the requirement that
n is less than +4.  Now go all the way back to the original problem and substitute
zero for n. If you do that you get 
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{{{-2*(-8) > 4}}}
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The left side is +16 and the right side is +4.  +16 is greater than +4 so the inequality holds.
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Hope this gives you the idea of how to work inequalities.  You can do operations just as
you would do with an equation, but you must be careful about reversing the inequality
sign as was discussed previously.