SOLUTION: why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number.

Question 142561: why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number.
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a larger positive value (greater than) becomes a larger negative value (less than)
__ and vice versa
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number.
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Draw a number line.
Plot the points x = -2 and x = +3
Notice that -2 is to the left of +3, so -2 < +3
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Now multiply both numbers by -5 and see what happens:
The -2 becomes +10 and the +3 becomes -15
Plot those points on the number line. Notice
that the -15 is to the left of +10 so -5*+3 < -5*-2:
the order has switched because you multiplied by a negative.
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Cheers,
Stan H.

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