Answer:
![x\geq 7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lqbyzyluhdk0x926cxiald9uy7mdti4mqc.png)
Explanation:
Given
![|2x+3|\geq |x-7|](https://img.qammunity.org/2020/formulas/mathematics/college/8luvcoo5tov50229ufunbq9wrqfzem4cn4.png)
here we will divide x interval in 3 case
case
![x<(-3)/(2)](https://img.qammunity.org/2020/formulas/mathematics/college/hcky0rzcadr7aru7zw8nr0uav2ayighm5t.png)
let us take x=-2
|-1| is not greater than |-9|
thus
is not possible
Case
![(-3)/(2)<x<7](https://img.qammunity.org/2020/formulas/mathematics/college/zcxtbii5rn4zf4wpzwx820dmqdyzq1d49j.png)
Take x=0
|3| is less than |-7|
thus for
equality is not satisfied
Case 3
![x\geq 7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lqbyzyluhdk0x926cxiald9uy7mdti4mqc.png)
take x=7
|17| is greater than |0|
Thus for
is the required region