Question

Solve the compound inequality

Answer 1

x ≤ -3 or x ≥ 9

Step-by-step explanation:

Hello!

We can solve for x in both inequalities that are given.

6x ≤ -18

• 6x ≤ -18
• x ≤ -18/6
• x ≤ -3

9x ≥ 81

• 9x ≥ 81
• x ≥ 81/9
• x ≥ 9

The answer is the first option: x ≤ -3 or x ≥ 9.

Tip:
If you have an inequality with a negative coefficient, such as -3x ≤ 6, when dividing a number by a negative number, you have to flip the inequality.

• -3x ≤ 6
• x ≥ 6/-3
• x ≥ -2

Answer 2

Answer: Choice A)
`\boldsymbol{x \le -3} \textbf{ or } \boldsymbol{x \ge 9}`

===================================================

Step-by-step explanation:

Let's solve the first inequality mentioned.

To do so, divide both sides by 6.

`6x \le -18\\\\6x/6 \le -18/6\\\\x \le -3`

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:

`9x \ge 81\\\\9x/9 \ge 81/9\\\\x \ge 9`

So overall
`\boldsymbol{x \le -3} \ \textbf{ or } \ \boldsymbol{x \ge 9}`

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.