The problem asks us to find the graph that represents the solution to the inequality $5 + 8x < 3(2x+4)$.

1. Problem Description

The problem asks us to find the graph that represents the solution to the inequality $5 + 8x < 3(2x+4)$.

2. Solution Steps

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

$5 + 8x < 3(2x+4)$

$5 + 8x < 6x + 12$

$8x - 6x < 12 - 5$

$2x < 7$

$x < \frac{7}{2}$

$x < 3.5$

Now, we look for the graph that represents $x < 3.5$. This means we need a number line with an open circle at 3.5, and the arrow should point to the left (towards smaller values).

Option A has a closed circle at a negative value, so it is incorrect.

Option B has an open circle at 3.5 and the arrow points left. This is a possible solution.

Option C has an open circle at 4, so it is incorrect.

Option D is a number line but doesn't have an open or closed circle and an arrow so it is incorrect.

Therefore, option B is the correct solution.

3. Final Answer

B