Answer:[tex]x\geq 7[/tex]
Step-by-step explanation:
Given
[tex]|2x+3|\geq |x-7|[/tex]
here we will divide x interval in 3 case
case [tex]x<\frac{-3}{2}[/tex]
let us take x=-2
|-1| is not greater than |-9|
thus [tex]x<\frac{-3}{2}[/tex] is not possible
Case [tex]\frac{-3}{2}<x<7[/tex]
Take x=0
|3| is less than |-7|
thus for [tex]\frac{-3}{2}<x<7[/tex] equality is not satisfied
Case 3 [tex] x\geq 7[/tex]
take x=7
|17| is greater than |0|
Thus for[tex]x\geq 7[/tex] is the required region
