The problem asks to find the number line that represents the solution to the inequality $-3x + 7 \ge 19$.

1. Problem Description

The problem asks to find the number line that represents the solution to the inequality $-3x + 7 \ge 19$.

2. Solution Steps

First, we need to solve the inequality for $x$.

$-3x + 7 \ge 19$

Subtract 7 from both sides:

$-3x + 7 - 7 \ge 19 - 7$

$-3x \ge 12$

Divide both sides by -

3. Since we are dividing by a negative number, we need to flip the inequality sign:

$\frac{-3x}{-3} \le \frac{12}{-3}$

$x \le -4$

Now we need to find the number line that represents $x \le -4$. This means we need a closed circle (or solid dot) at -4, and the line should extend to the left (towards negative infinity).

Looking at the options, the second number line has a closed circle at -4, and the arrow extends to the left.

3. Final Answer

The second number line shows the solution to the inequality.