Option D:
[tex]x<-9 \text { or } x \geq 6[/tex]
Solution:
Given compound inequality:
[tex]6-x>15 \text { or } 2 x-9 \geq 3[/tex]
Let us first solve [tex]6-x>15[/tex].
Subtract 6 from both sides.
[tex]6-x-6>15-6[/tex]
[tex]-x>9[/tex]
To reverse the inequality multiply by -1 on both sides.
[tex](-x)(-1)<9(-1)[/tex]
[tex]x<-9[/tex]
Now solve the next inequality [tex]2 x-9 \geq 3[/tex].
Add 9 on both sides.
[tex]2 x-9+9 \geq 3+9[/tex]
[tex]2 x \geq 12[/tex]
Divide by 2 on both sides.
[tex]$\frac{2 x}{2} \geq \frac{12}{2}[/tex]
[tex]x \geq 6[/tex]
Combine the inequality.
[tex]x<-9 \text { or } x \geq 6[/tex]
Option D is the correct answer.
