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Most important point is the roots of this equation in absolute value brackets. For this|2x +3| root is -3/2 (-3/2.2 + 3 =0) So -3/2 is a crucial point. When x is less than this value, value in the bracket becomes negative and vice versa
[quote="amit2k9"]1. To solve which kind of inequalities determining crucial point becomes neccessary. 2.In this equation how to determine the crucial point (point at which the sign changes)? |2x +3|> x +6.
2x+3<-x-6 ie: 3x<-9 ie: x<-3 ie: the inquality is not defined in the range -3 to 3 and any other number satisfy it
in this case, crucial points are 3 and -3. and to decide what is the range just put the values -10, 10 and 0. n u will notice that this inequality is satisfied only when x >0 or x< - 3. just putting -10, 0 n 10 in the orginal eq, this range can be verified.