Solve the inequality and graph the solution.

Question

1≥
h–2
2
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

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

1. Endpoints: The endpoints of the interval is at \( h = 4 \).
2. Closed/Open Interval: Since \( h \leq 4 \) includes \( 4 \), the endpoint at \( h = 4 \) will be a closed circle.
3. 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 \( 4 \).