Final answer:
To solve an absolute value equation, identify knowns, define a positive direction, algebraically define vectors, solve the equation, substitute known values to obtain solutions, and check that the answer is reasonable.
Step-by-step explanation:
To solve absolute value equations effectively, it is important to follow a systematic approach. This method helps to ensure accuracy and to verify that the obtained solutions are reasonable. When Misha's group is solving such equations, take note of the given steps below and arrange them in a logical sequence, making sure that each step precedes logically from the one before it.
- Make a list of what is given or can be inferred from the problem as stated (identify the knowns).
- Choose a positive direction for your coordinate system.
- Algebraically define your vectors based on the chosen coordinate system.
- Solve the appropriate equation for the quantity to be determined (the unknown).
- Substitute the known values along with their units into the appropriate equation and obtain numerical solutions complete with units. Be sure to include absolute values for temperature and pressure if necessary.
- Check the answer to see if it is reasonable: Does it make sense? Are the units correct and are the numbers involved reasonable?
By executing these steps in order, students can systematically find solutions to absolute value equations, while the final verification step ensures that their solutions are logical within the context of the problem.