We are asked to solve the absolute value equation $|5x + 4| + 10 = 2$ for $x$.

1. Problem Description

We are asked to solve the absolute value equation $|5x + 4| + 10 = 2$ for $x$.

2. Solution Steps

First, isolate the absolute value expression by subtracting 10 from both sides of the equation:

$|5x + 4| + 10 - 10 = 2 - 10$

$|5x + 4| = -8$

The absolute value of any expression is always non-negative (i.e., greater than or equal to zero). In this case, we have that the absolute value of $5x + 4$ is equal to $-8$, which is a negative number. Since an absolute value cannot be negative, there is no solution to the given equation.

3. Final Answer

No solution.