Key Concepts:
- A variable can be solved by applying inverse operations such as addition, subtraction, multiplication, division, and taking square roots.
- Zero-Product Property: If (ab = 0), then either (a = 0) or (b = 0), a fundamental tool for solving factored equations.
- Equations involving absolute values (e.g. (|x - 2| = 3)) can be solved by considering two cases (e.g. (x - 2 = 3) and (x - 2 = -3)).
Skills Covered:
- Manipulating and simplifying algebraic equations.
- Using the zero-product property to solve factored equations.
- Solving quadratic equations using factoring or taking square roots (e.g., solving (x^2 = 16) gives (x = \pm 4)).
- Understanding and solving absolute value equations.
Example Problems:
- Solve for x in (x^2 - 9 = 0).
- Factor and solve (x^2 - 7x + 10 = 0).
- Solve (|3x - 5| = 7).