MA19.PRE.20
Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a clear-cut solution. Construct a viable argument to justify a solution method. Include equations that may involve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric functions, and their inverses.
Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a clear-cut solution. Construct a viable argument to justify a solution method. Include equations that may involve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric functions, and their inverses.
Unpacked Content
UP:MA19.PRE.20
Vocabulary
- equivalence
- viable
Knowledge
- How to solve equations using a reasoning process centered around inverse operations and order of operations
Skills
- Solve linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equations (including their inverses) using multiple solution strategies and explain each step in the solution path.
- Construct a viable argument to justify a chosen solution path used to solve a linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, and trigonometric equation (including their inverses).
- Compare the steps in each and determine which solution path is most efficient, given an equation with multiple solution paths.
- Explain when an equation has no solution or infinitely many solutions.
Understanding
- The process of solving equations is a reasoning process to determine a solution that satisfies the equation rather than a procedural list of steps.
- An equation has no solution because there is no value that can maintain equivalency and an equation has infinitely many solutions because all values used for the variable create a true equivalency statement