Question 133421
Why does the inequality sign change when both sides are multiplied or divided by a negative number?
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Draw a number line.
Put a dot at x = 2 and at x = 10
Notice that 10 is to the right of 2 which means 10 > 2
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Multiply both by -1 to get -2 and -10.
Put those points on the same number line.
Notice that the -10 is to the left of -2 which mean -10 < -2
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That is why you must change the inequality sign when you multiply
by a negative; dividing by a negative is the same as multiplying
by a negative fraction.
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Does this happen with equations? Why or why not?
Yes, the same thing happens with equations; the inequality sign switches.
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Write an inequality for your class to solve. In your inequality, use both the multiplication and addition properties of inequalities.  Explain how you arrived at your answer.
-2x +7 < 10  
Subtract 7 from both sides to get:
-2x < 3
Divide both sides by -2 to get:
x > -3/2
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Cheers,
Stan H.