To solve the inequality [tex]\(\frac{1}{2} x \leq 18\)[/tex], follow these steps:
1. Identify the inequality:
[tex]\[
\frac{1}{2} x \leq 18
\][/tex]
2. Eliminate the fraction:
To isolate [tex]\(x\)[/tex], multiply both sides of the inequality by 2:
[tex]\[
2 \times \left( \frac{1}{2} x \right) \leq 2 \times 18
\][/tex]
This simplifies to:
[tex]\[
x \leq 36
\][/tex]
3. Interpret the solution:
The inequality [tex]\(x \leq 36\)[/tex] indicates that the solution set includes all values of [tex]\(x\)[/tex] that are less than or equal to 36.
4. Graph the solution on the number line:
- Draw a number line.
- Locate the point 36 on the number line.
- Use a closed circle at 36 to indicate that 36 is included in the solution set.
- Shade the number line to the left of 36 to represent all values less than 36.
The graph representing the solution set for the inequality [tex]\(\frac{1}{2} x \leq 18\)[/tex] will show a closed circle at 36 and shading to the left of 36. This visual representation confirms that all numbers less than or equal to 36 satisfy the inequality.
