Solve the inequality set and graph the solution on a number line.

Inequalities:
1. [tex]x + 14 \ \textgreater \ 16[/tex]
2. [tex]x + 9 \leq 16[/tex]

Choose the correct solution:
A. [tex]x \leq 2[/tex] and [tex]x \ \textgreater \ 7[/tex]
B. [tex]x \ \textgreater \ 2[/tex] and [tex]x \leq 7[/tex]
C. [tex]x \leq 7[/tex]
D. [tex]x \ \textgreater \ 2[/tex]
E. All real numbers
F. No solution

We want to solve the system of inequalities:
[tex]$$
x + 14 > 16 \quad \text{and} \quad x + 9 \le 16.
$$[/tex]

Step 1. Solve the first inequality:
[tex]\[
x + 14 > 16
\][/tex]
Subtract 14 from both sides:
[tex]\[
x > 16 - 14 \quad \Longrightarrow \quad x > 2
\][/tex]

Step 2. Solve the second inequality:
[tex]\[
x + 9 \le 16
\][/tex]
Subtract 9 from both sides:
[tex]\[
x \le 16 - 9 \quad \Longrightarrow \quad x \le 7
\][/tex]

Step 3. Find the intersection:

Since both conditions must be satisfied, the solution is the set of numbers that are greater than 2 and at the same time less than or equal to 7:
[tex]\[
x > 2 \quad \text{and} \quad x \le 7.
\][/tex]

Step 4. Graph the solution on a number line:

To graph the solution, draw a number line marking the points 2 and 7. Place an open circle at 2 (since [tex]$x$[/tex] must be strictly greater than 2) and a closed circle at 7 (since [tex]$x$[/tex] can equal 7). Then shade the line between these points.

The final answer is:
[tex]$$
x > 2 \text{ and } x \le 7.
$$[/tex]

This corresponds to the third option from the given choices.