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Question 581129: Hi. I would like to know about this problem. -8x+3 greater than or equal to 27. Thank you.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
Adding (-3) to both sides (or subtracting 3 from both sides), the greater than or equal relationship is still true, so
 --> 
Multiplying (or dividing) both sides by a positive number maintains the inequality relationship, but multiplying (or dividing) both sides by a negative number reverses it. If we multiply both sides by  (or divide both sides by  ),
transforms into the equivalent 
That  is optional, of course.
You could write  and no one should object.
Then you just do the  division and end up with
You can verify by seeing, for example, that x=-3, and x=-4 are solutions of the original inequality, but x=0 is not.
If multiplying by negative numbers when solving inequalities makes you nervous, you can go the long way around it, just adding stuff and only multiplying/dividing by positive numbers, like this
-->  -->  -->  -->  -->  --> 
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