The problem requires us to solve the inequality $b + 45 \ge 48$ and then graph the solution on a number line.

1. Problem Description

The problem requires us to solve the inequality $b + 45 \ge 48$ and then graph the solution on a number line.

2. Solution Steps

First, we need to isolate the variable $b$ by subtracting 45 from both sides of the inequality:

$b + 45 \ge 48$

$b + 45 - 45 \ge 48 - 45$

$b \ge 3$

The solution to the inequality is $b \ge 3$. This means that $b$ can be any number greater than or equal to

3. To graph this on a number line, we need to put a closed circle (because of the "greater than or equal to" sign) at 3, and then draw an arrow to the right, indicating that all values greater than 3 are included in the solution.

3. Final Answer

The solution to the inequality is $b \ge 3$.

The graph should have a closed circle at 3 and an arrow pointing to the right.