Let's solve the given inequality step-by-step.
The given inequality is:
[tex]$ -9 > 2x $[/tex]
To isolate [tex]\( x \)[/tex], we need to solve for [tex]\( x \)[/tex]. We can start by dividing both sides of the inequality by 2:
[tex]\[
\frac{-9}{2} > x
\][/tex]
This results in:
[tex]\[
x < \frac{-9}{2}
\][/tex]
Simplifying [tex]\(\frac{-9}{2}\)[/tex] gives us:
[tex]\[
\frac{-9}{2} = -4.5
\][/tex]
Therefore, the inequality becomes:
[tex]\[
x < -4.5
\][/tex]
So, we can see that the solution to the inequality is [tex]\( x \)[/tex] being less than [tex]\(-4.5\)[/tex]. This corresponds to the choice:
(A) [tex]\( x < -\frac{9}{2} \)[/tex]
