The given model is 4x - 6x = 7. To determine if the model is stable, unstable, or neutrally stable (neutrally unstable), we need to analyze the behavior of the system.
First, let's rewrite the equation as a standard form: 4x = 6x + 7.
To determine stability, we can look at the sign of the coefficient in front of x. In this case, the coefficient is positive, which means that the system is unstable.
To understand why, let's consider an example. Suppose we have a small perturbation from the equilibrium point (where x = 0). If we substitute x = 0 + ε into the equation, where ε is a small positive number, we get 4x = 6(0 + ε) + 7, which simplifies to 4x = 7.
This means that the system will move away from the equilibrium point with time. The positive coefficient indicates that the system's behavior is unstable, as any small perturbation will cause the solution to grow indefinitely.
Therefore, the given model 4x - 6x = 7 is unstable.
Please let me know if there is anything else I can help you with.