Find the solution of |x-1| + |x-2| > |x| [ Answer : (-?, 1) U (3, ?) ] Share with your friends Share 0 Neha Sethi answered this Dear student We havex-1+x-2>xTesting each absolute for its positive and negative values.Consider x-1x-1≥0x≥1⇒For x≥1 , x-1=x-1 For x-1<0 , x<1⇒ For x<1 x-1=-x-1Consider x-2x-2≥0x≥2⇒For x≥2 , x-2=x-2For x-2<0 , x<2⇒ For x<2 ,x-2=-x-2So the following ranges are:x<0, 0≤x<1, 1≤x<2, x≥2For x<0Replacing x-1 with -x-1Replacing x-2 with -x-2Replacing x with -xSo, we get-x-1-x-2>-x-x+1-x+2>-x-x>-3x<3For 0≤x<1Replacing x-1 with -x-1Replacing x-2 with -x-2Replacing x with xSo, we get-x-1-x-2>x-x+1-x+2>x-2x>-3+x-3x>-3x<1For 1≤x<2Replacing x-1 with x-1Replacing x-2 with -x-2Replacing x with xx-1-x-2>xx-1-x+2>xx<1For x≥2Replacing x-1 with x-1Replacing x-2 with x-2Replacing x with xx-1+x-2>x2x-3>xx>3Combining the ranges x<0 and x<3 or 0≤x<1 and x<1 or 1≤x<2 and x<1 or x≥2 and x>3we getx<1 or x>3Interval Notation: -∞,1∪3,∞ Regards 0 View Full Answer
