Which of the following is not the solution of
`|2x+5|-|x-3| ge |x+8| ` ?

Options

A. `(-oo,-8]`
B. `[3,oo)`
C. `(-8,3)`
D. none of these

Answer

C

Explanation

`(c )` `|2x+5|-|x-3| ge |x+8|`
`implies |2x+5|-|x-3| ge |(2x+5)-(x-3)|`
`implies (2x+5)(x-3) ge 0 implies -x le -(5)/(2)` or `x ge 3` .........`(i)`
Also `|2x+5| ge |x-3|`
Squaring both sides,
`4x^(2)+20x+25 ge x^(2)-6x+9`
`implies3x^(2)+26x+16 ge 0`
`implies (3x+2)(x+8) ge 0`
`implies x le -8` or `x ge -(2)/(3)`..........`(ii)`
From `(i)` and `(ii)` , `x in (-oo,-8]uu[3,oo)`