Consider the following inequality.

−2x≥18

Step 2 of 2 :  Graph the solution to the given inequality.

Let's solve the inequality first:

### Step 1: Solve for \( x \)
The inequality is:
\[
-2x \geq 18
\]

To isolate \( x \), divide both sides by \( -2 \). Remember that when you divide or multiply an inequality by a negative number, the direction of the inequality reverses:

\[
x \leq \frac{18}{-2}
\]
\[
x \leq -9
\]

So, the solution is:
\[
x \leq -9
\]

### Step 2: Graph the solution

On a number line:

1. Draw a solid dot at \( x = -9 \) because the inequality includes \( -9 \) (i.e., \( \leq \)).
2. Shade the portion of the number line to the left of \( -9 \) to represent all values less than or equal to \( -9 \).

This shows that the solution includes \( -9 \) and all values less than \( -9 \).

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Would you like a visual representation of this graph? If you have any questions or need clarification, feel free to ask!

Here are 5 related questions:
1. How would the graph change if the inequality were \( -2x > 18 \)?
2. What happens if you multiply both sides of an inequality by a positive number instead of a negative one?
3. Can you explain why the inequality sign reverses when dividing by a negative number?
4. What is the difference between a solid dot and an open dot on a number line graph?
5. How would the solution change if the inequality was \( -2x \leq 18 \)?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Consider the following inequality. −2x ≥ 18. Step 2 of 2: Graph the solution to the given inequality.

Learn how to graph the solution for the inequality -2x ≥ 18. This problem involves understanding algebraic inequalities, dividing by negative numbers, and graphing solutions on a number line. Suitable for students in Grades 7-9.

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