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Resuelve el problema de reglas de signos 

The image provides a math problem that asks for the resolution of two equations and the corresponding values on the number line. The equations are:

1. \( a + 4x = 0 \)
2. \( b - 4(x - 4) = 0 \)

Below the number line is labeled from -8 to 8, and the task likely involves solving these equations and placing the solutions on this number line.

Let's solve the equations step by step:

### Equation 1: \( a + 4x = 0 \)
1. Solve for \( x \):
   \[
   4x = -a \quad \Rightarrow \quad x = -\frac{a}{4}
   \]
   The solution depends on the value of \( a \), but without a specific \( a \), this gives a general solution.

### Equation 2: \( b - 4(x - 4) = 0 \)
1. Simplify and solve for \( x \):
   \[
   4(x - 4) = b \quad \Rightarrow \quad x - 4 = \frac{b}{4} \quad \Rightarrow \quad x = \frac{b}{4} + 4
   \]
   Again, the exact solution depends on \( b \).

To proceed further, you'd need specific values for \( a \) and \( b \) to plot on the number line. Do you have these values, or should we work with potential examples? Let me know if you'd like further details! 

Here are 5 related questions:

1. How does changing the value of \( a \) affect the solution in the first equation?
2. What happens if \( b = 0 \) in the second equation?
3. How can these solutions be verified using substitution?
4. How would the number line change if \( x \) were multiplied by a different coefficient?
5. Can you find additional equations that result in solutions between -8 and 8?

**Tip:** When solving linear equations, isolating the variable on one side simplifies the process greatly.

Aprende a resolver problemas de reglas de signos en ecuaciones lineales con una solución detallada paso a paso. Este problema incluye conceptos clave como la resolución de ecuaciones lineales y el uso de la línea numérica. Adecuado para estudiantes de grados 7-9.

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