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Question
I was having a hard time with this homework problem and my answer doesn't match with the multiple choice I got. Here it goes:

Question:

Solve: 2-3x<8 and 2x-3 is greater than or equal to -9.

Answers:
A. -2<x is less than or equal to -3
B. x<-2 and x is greater than or equal to -3
C. X>-2
D. X<-2

Answer
For negative signs, the key thing to remember is to reverse the sign on negative multiplication or division.

For 2-3x<8, subtract 2 from both sides.  This gives -3x<6.
Divide both sides by -3, giving x>-2.  Note that when x=-2 is put in, you get 8.
From here, it can be seen that any x>-2 satisfies the inequality.

For 2x-3>-9, add 3 to both sides.  This gives 2x > -6.
Divide both sides by 2, giving x > -3.
Againg, if x=-3 is put in, the result is -6-3 = -9 is gotten.

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Scott A Wilson

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