Final answer:
To solve the equation 4x = -4x, you can graph y = 4x and y = -4x, but it's also clear algebraically that the equation is always true. Therefore, it's an identity with an infinite number of solutions.
Step-by-step explanation:
To find the solution(s) to the equation 4x = –4x, you could graph two functions, y = 4x and y = –4x, and look for their intersection points. However, without graphing, we can see that adding 4x to both sides gives 0 = 0, which tells us that this equation is true for all values of x, suggesting an infinite number of solutions or that the equation is an identity.
In cases where algebraic methods are difficult, solving models with graphs can be an alternative approach. For instance, graphing equations to find the equilibrium price and quantity in economics, or using a graph to visualize the solutions to quadratic equations.