SOLUTION: Could you give me an example of why the inequality sign changes when both sides are multiplied or divided by a negative number? I just don't understand and hope you can give me som
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Question 176364: Could you give me an example of why the inequality sign changes when both sides are multiplied or divided by a negative number? I just don't understand and hope you can give me some examples.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
All points to the right of x=1 satisfy that equation.
Now multiply the equation by (-1) and don't change the sign.
2.
Now pick a point in the region that satisfies the original equation.
Let's pick x=3 and plug it into eq. 2,
2.
Clearly -3 is not greater than -1.
So you cannot satisfy both eq. 1 and eq. 2 because you have not changed the sign of the inequality.
Not changing the sign leads to incorrect results, hence the reason the inequality sign needs to be changed.
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