|3x + 1| > |2x + 2| This is what I have so far: Case 1: positive = positive 3x + 1 > 2x + 2 x > 1 BUT 3x + 1 > 0 therefore x > -1/3 BUT 2x + 2 > 0 therefore x > -1 FINAL CONDITION: x > -1 Case 2: negative = positive -3x - 1 > 2x + 2 -5x > 3 x < -3/5 BUT 3x + 1 < 0 therefore x < -1/3 BUT 2x + 2 > 0 therefore x > -1 FINAL CONDITION: -1 < x < -1/3 Case 3: positive = negative 3x + 1 > -2x - 2 5x > -3 x > -3/5 BUT 3x + 1 > 0 therefore x > -1/3 BUT 2x + 2 < 0 therefore x < -1 FINAL CONDITION: I am confused for this final condition, because if you graph it on a number line, you'll get a domain for x > -1/3 but than for this FINAL CASE x < -1 which confuses me because it doesn't intersect with the other domains of X in that final case, so what would the final condition for that case be and what would the FINAL CONDITION for the whole question be? Thank you for any and all help

That is the way I was thought :S because sometimes in absolute value graphs, certain branches DO NOT intersect, and you have to do this to find out which region is below or above which region etc. How did you arrive at the answer x > 1? Thanks for your help