1. The problem is to understand the inequalities involving the variable $b$ and how they relate to the number line from 5 to 15. 2. The inequalities given are: - $b > 8$: $b$ is greater than 8. - $b \geq 8$: $b$ is greater than or equal to 8. - $b < 8$: $b$ is less than 8. - $b \leq 8$: $b$ is less than or equal to 8. 3. On the number line from 5 to 15: - For $b > 8$, $b$ includes all numbers strictly greater than 8 (9, 10, 11, ...). - For $b \geq 8$, $b$ includes 8 and all numbers greater than 8. - For $b < 8$, $b$ includes all numbers less than 8 (5, 6, 7). - For $b \leq 8$, $b$ includes 8 and all numbers less than 8. 4. These inequalities describe intervals on the number line: - $b > 8$ corresponds to $(8, \infty)$. - $b \geq 8$ corresponds to $[8, \infty)$. - $b < 8$ corresponds to $(-\infty, 8)$. - $b \leq 8$ corresponds to $(-\infty, 8]$. 5. Understanding these inequalities helps in graphing and solving problems involving ranges of values for $b$.