We are asked to solve the linear equation $5x + 4 = -2x - 24$ for the variable $x$.

1. Problem Description

We are asked to solve the linear equation $5x + 4 = -2x - 24$ for the variable $x$.

2. Solution Steps

We start with the given equation:

$5x + 4 = -2x - 24$

Add $2x$ to both sides of the equation:

$5x + 2x + 4 = -2x + 2x - 24$

$7x + 4 = -24$

Subtract 4 from both sides of the equation:

$7x + 4 - 4 = -24 - 4$

$7x = -28$

Divide both sides of the equation by 7:

$\frac{7x}{7} = \frac{-28}{7}$

$x = -4$

3. Final Answer

The solution to the equation is $x = -4$.