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- 55

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|x-1|-|x|+|2x+3| > 2x+4

Well in one of its solutions we were told to apply the method of intervals, rather than taking say what; like 8 combination of signs.

For everyone of its intervals(say -3/2 [itex]\leq[/itex]x <0) we are said that 2x+3 [itex]\geq[/itex] 0, x<0 and x-1<0.

Is it just an intuitive outcome(guessing by the extremities of the limits) or did we do something to predict what the signs of the expressions will be?(as i was wondering if any such intervals, which violated an intuitive outcome ?)