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How do I know when the answer to an equation is negative?

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2 Answers

There isn't really a solid way of knowing whether an answer will be negative or positive. The best way to know is just to solve. But to quickly have a sketch in mind you can throw all the constants to one side and x factor to the other and if either will turn out negative and the other positive then it's negative or if both are positive or both negative then the answer will be positive. 

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This one is fairly easy because the terms are all positive, and the right side has more "x" quantities and a higher number, or "constant," than the left side. The answer will be negative.

To make sure, you can solve it:

     x + 22  =  3x + 45

First, subtact 1x from both sides:

     x + 22  =  3x + 45
    -x              -x
_______________________
           22  =  2x + 45

Now subtract 45 from both sides:

            22  =  2x  + 45
          -45              - 45
--------------------------------
           -23  =  2x

Divide both sides by 2. Your answer is:

          x = -23/2  or   -11.5


You can usually figure out short problems like this one mentally, but it's always best to go through the steps to be sure.

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