Question 11. 2 x + 3 - 2 x - 5 = 6 Share with your friends Share 0 Neha Sethi answered this Dear student 2x+3-2x-5=6Testing each absolute for its positive and negative ranges.2x+3≥0 ⇒2x≥3⇒x≥-322x+3<0 for x<-32 So, for x<-32 2x+3=-2x+32x-5≥0⇒2x≥5⇒x≥522x-5≥0 for x≥52 , So for x≥52 |2x-5|=2x-52x-5<0⇒2x<5⇒x<522x-5<0 for x<52, so for x<52 2x-5=-2x-5Evaluating the expression in following rangesx<-32, -32≤x≤52, x≥52For x<-32Replacing 2x+3 with -2x+3Replacing 2x-5 with -2x-5-2x+3--2x-5=6-2x-3+2x-5=6-8=6Since RHS and LHS are not equal ,so no solution for x∈R.For -32≤x≤52Replacing 2x+3 with 2x+3Replacing 2x-5 with -2x-52x+3--2x-52x+3+2x-5=64x-2=64x=8x=2For x≥52Replacing 2x+3 with 2x+3Replacing 2x-5 with 2x-52x+3-2x-5=62x+3-2x+5=68=6Since RHS and LHS are not equal ,so no solution for x∈R.Combining ranges -32≤x≤52 and x=2x=2 Regards 1 View Full Answer Poornima Singh answered this Please find this answer -2
