Final answer:
To write an algebraic expression to model quantities, start by assigning variables to unknowns, identify knowns and unknowns, solve and simplify the equations, substitute known values with units, and finally, check if the solution is reasonable.
Step-by-step explanation:
To write an algebraic expression that models quantities, you should start by identifying and assigning variables to unknown quantities. This process involves several steps:
- Identifying the knowns: Determine what information is given or can be inferred from the problem.
- Identifying the unknowns: Define what needs to be solved for in the problem.
- Solve the appropriate equation or equations to find the unknown quantity.
- Substitute the known values along with their units into the equation to obtain a numerical solution, complete with units. It is essential to use the correct units, for example, radians for angles.
- Eliminate terms wherever possible to simplify the algebra.
- Always check if your answer is reasonable: Confirm that the result makes sense in the context of the problem.
The use of symbols in algebra is arbitrary, and by practicing this method, you will understand that algebraic expressions are just a way to capture a concept mathematically. Working through these steps collaboratively or independently allows you to apply basic algebra and arithmetic principles to model various quantities effectively.