The problem asks to solve for $x$ in the equation $8(\frac{1}{2}x - 5) - 3 = 3(x + 15)$.

1. Problem Description

The problem asks to solve for $x$ in the equation $8(\frac{1}{2}x - 5) - 3 = 3(x + 15)$.

2. Solution Steps

First, we distribute the constants on both sides of the equation.

$8(\frac{1}{2}x - 5) - 3 = 3(x + 15)$

$8 \cdot \frac{1}{2}x - 8 \cdot 5 - 3 = 3x + 3 \cdot 15$

$4x - 40 - 3 = 3x + 45$

$4x - 43 = 3x + 45$

Next, we isolate $x$ by subtracting $3x$ from both sides.

$4x - 43 - 3x = 3x + 45 - 3x$

$x - 43 = 45$

Finally, we add 43 to both sides to solve for $x$.

$x - 43 + 43 = 45 + 43$

$x = 88$

3. Final Answer

$x = 88$