Question

You found that x = 9 is the boundary point. That is the point that separates numbers that are solutions from numbers that are not solutions. What is the solution to the inequality?

x= 8

x= 9 (boundary)

x= 10

-2x

 ≥ -18truetruefalse

-2x

 ≥ -18
x 

 

>

≥

<

≤

 

Answer 1

To solve the inequality \(-2x \geq -18\), follow these steps:

1. **Isolate \(x\)**:
- Divide both sides of the inequality by \(-2\). Remember that when you divide or multiply both sides of an inequality by a negative number, you must flip the inequality sign.

\[
-2x \geq -18 \implies x \leq 9
\]

2. **Identify the boundary point**:
- The boundary point is \(x = 9\). That is where the inequality changes from true to false.

3. **Determine the solution**:
- The solution to the inequality is all \(x\) values that are less than or equal to 9.

**Final Solution**:
- \(x \leq 9\)

In interval notation, this can be represented as:
- \((-\infty, 9]\)

This means, all numbers less than or equal to 9 (including 9) are solutions to the inequality.

**Additional Notes**:
- The inequality \(-2x \geq -18\) does not include values greater than 9 as solutions. Hence, \(x = 8\) is part of the solution set while \(x = 10\) is not.