To solve the inequality:
\[ 1 \geq \frac{h - 2}{2} \]
First, we can eliminate the fraction by multiplying both sides by 2 (note that since 2 is positive, the inequality direction remains the same):
\[ 2 \geq h - 2 \]
Next, we can add 2 to both sides of the inequality:
\[ 2 + 2 \geq h \]
This simplifies to:
\[ 4 \geq h \]
or equivalently:
\[ h \leq 4 \]
Now we interpret the inequality \( h \leq 4 \). The solution set includes all values of \( h \) that are less than or equal to 4.
Graphing the Solution
- Endpoints: The endpoints of the interval is at \( h = 4 \).
- Closed/Open Interval: Since \( h \leq 4 \) includes \( 4 \), the endpoint at \( h = 4 \) will be a closed circle.
- Resulting Graph:
- Shade to the left of \( h = 4 \) to indicate all values \( h \) that are less than or equal to \( 4 \) should be included.
- You will have a closed circle at \( h = 4 \).
Conclusion
The solution is:
\[ (-\infty, 4] \]
Where \( 4 \) is included in the solution set. The graphical representation will include a closed circle at \( h = 4 \), and the shading will extend to the left, indicating all values up to and including \( 4 \).