Final answer:
The C) algebraic method is used to solve compound inequalities step by step, offering more accuracy than the graphical method, which can be limited by the drawing's precision. Calculators like the TI-83, 83+, or 84 can perform these algebraic computations.
Step-by-step explanation:
The process used to solve compound inequalities step by step is the algebraic method. This involves a series of algebraic steps to find the solution set. For compound inequalities, one might use a calculator that could handle such algebraic manipulations. Models like the TI-83, 83+, or 84 are capable of this and may provide a function specific to solving inequalities.
However, it is essential to understand that while graphical methods can be used to solve inequalities by providing a visual representation, the algebraic method typically offers a more precise solution. This is because with the graphical method, the accuracy is limited by the precision of the drawing or the scale of the graph, which can be problematic when needing exact solutions.
When looking at vector addition as an example, analytical techniques are preferred for precision. Graphical methods, though useful for a visual understanding, may only offer an approximate solution when it comes to detailed calculations or when dealing with trigonometry. Still, it is worth noting that graphical methods assume data from graphs to be accurate to three digits, which can be sufficient for some applications. Therefore, when precision is key, such as in technical or scientific contexts, the algebraic method is favored.