How do you solve # |2x - 1 | - |3x + 2| = 2 #?

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Answer 1 · 2015-07-23T17:16:55

Verify these numbers: #-5, 1/5, -3/5, -1#

#|2x-1| = 2 + |3x + 2|#

#S = ±1 \Rightarrow 2x-1 = 2S + |3x + 2|S#

#(2x-1 - 2S)/S = |3x + 2|#

#T = ±1 \Rightarrow (2x-1 - 2S)/S cdot T = 3x + 2#

#2Tx-T - 2ST = 3Sx + 2S#

#(2T-3S)x = T + 2ST + 2S#

#x = (T + 2ST + 2S)/(2T-3S)#

#x_11 = (1 + 2 + 2)/(2-3)#

#x_{1,-1} = (-1 - 2 + 2)/(-2-3)#

#x_{-1,1} = (1 - 2 - 2)/(2+3)#

#x_{-1,-1} = (-1 + 2 - 2)/(-2+3)#