Answer: Choice A) [tex]\boldsymbol{x \le -3} \textbf{ or } \boldsymbol{x \ge 9}[/tex]
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Explanation:
Let's solve the first inequality mentioned.
To do so, divide both sides by 6.
[tex]6x \le -18\\\\6x/6 \le -18/6\\\\x \le -3[/tex]
The inequality sign stays the same the entire time. It only flips if we divided both sides by a negative number.
Through similar steps, this is how we'd solve the second inequality given:
[tex]9x \ge 81\\\\9x/9 \ge 81/9\\\\x \ge 9[/tex]
So overall [tex]\boldsymbol{x \le -3} \ \textbf{ or } \ \boldsymbol{x \ge 9}[/tex]
The key word "or" is important. If it was "and", then we'd have no solutions because no such number is both smaller than -3 and also larger than 9 at the same time.
The graph of this on the number line will involve closed circles at -3 and 9. Then we shade anything that is not between those closed circles.
