Sure, let's work through the inequality step-by-step and determine how the solution set can be represented graphically.
1. Start with the given inequality:
[tex]\[
\frac{1}{2} x \leq 18
\][/tex]
2. Eliminate the fraction by multiplying both sides of the inequality by 2:
[tex]\[
2 \cdot \frac{1}{2} x \leq 18 \cdot 2
\][/tex]
[tex]\[
x \leq 36
\][/tex]
3. Interpret the result:
The inequality \(x \leq 36\) means that \(x\) can be any number less than or equal to 36.
4. Represent this solution set on a number line:
- Draw a number line.
- Identify and mark the point corresponding to \(x = 36\) on the number line.
- Shade or draw a solid line to the left of this point, indicating that all numbers less than 36 are included in the solution set.
- Draw a solid circle or closed dot at \(x = 36\), indicating that 36 is included in the solution set.
The graphical representation of the solution \(x \leq 36\) on a number line would look something like this:
[tex]\[
\begin{array}{ccccccccccccccccccccccccccc}
\leftarrow & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & - & \bullet & =====================) & 36
\end{array}
\][/tex]
In summary, the graph representing the solution set for the inequality [tex]\(\frac{1}{2} x \leq 18\)[/tex] is a number line with a solid line or shaded region extending to the left from 36, including 36 itself.
