We are asked to solve the inequality $28 + 4p \ge 8(6p - 2)$. The inequality represents a constraint on the possible values of the variable $p$. We need to find the range of values for $p$ that satisfy this inequality. We are also provided with a number line below the expression.

1. Problem Description

We are asked to solve the inequality $28 + 4p \ge 8(6p - 2)$. The inequality represents a constraint on the possible values of the variable $p$. We need to find the range of values for $p$ that satisfy this inequality. We are also provided with a number line below the expression.

2. Solution Steps

First, we distribute the 8 on the right side of the inequality:

$28 + 4p \ge 8(6p - 2)$

$28 + 4p \ge 48p - 16$

Next, we want to isolate the variable $p$. We can subtract $4p$ from both sides:

$28 + 4p - 4p \ge 48p - 16 - 4p$

$28 \ge 44p - 16$

Now, we add 16 to both sides:

$28 + 16 \ge 44p - 16 + 16$

$44 \ge 44p$

Finally, we divide both sides by 44:

$\frac{44}{44} \ge \frac{44p}{44}$

$1 \ge p$

This can also be written as $p \le 1$.

3. Final Answer

$p \le 1$