Question 771585: Jane is thinking of a number between -10 and 10. If you multiply Jane’s number by -2, then subtract 2, the result is greater than 6. Is Jane's number greater than -4 or less than -4?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The fact that the number is between -10 and 10 does not matter for the problem.
However, if you had to guess the number, knowing that it is between -10 and 10 would improve your chances.
THE GUESSER SOLUTION:
Could it be  ?
 and that is not greater than 6, so cannot be Jane's number.
Since is greater than -4, and it does not work, the solution must be that
Jane's number is less than -4
THE ALGEBRA SOLUTION:
 = the number Jane is thinking
 = the number Jane is thinking multiplied times 
 = the result of multiplying Jane's number times -2, and then subtracting 2
 -->  (taking out the common factor )
-->  (because on multiplying/dividing by a negative number we are flipping around the number line, and that flips the inequality sign, see NOTE below)
-->  (just simplifying)
-->  -->  (subtracting 1 from both sides and simplifying)
So Jane's number is less than -4.
NOTE:
 
The numbers to the left (of -4, or of any other number) are less, and the numbers to the right are more.
Multiplying times -1 means changing the signs off all the numbers, so we end up with
  or 
If one number was less than (to the left of) a certain number, after multiplying both numbers times -1, the order is reversed, so the signs change from < to > and from > to <.
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