In this work, a fuzzy linear equation AX + B = 0, is solved, were A, B y C are triangular diffuse numbers, could also be trapezoidal. For this type of equations there are several solution methods, the classic method that does not always obtain solutions, the most used is the method of alpha cuts and arithmetic intervals that although it always finds a solution, as a value is taken closer to zero (more inaccurate), the solution satisfies less to the equation. The new method using the expected interval, allows to obtain a smaller support set where the solutions come closer to satisfying the equation, also allows to find a single interval where the best solutions for decision making are expected to be found. It is recommended to study the incorporation of the concept of the expected interval in the methods to solve systems of fuzzy linear equations