Understands and applies equations and inequalities
An equation involves the relationship of "equals" (e.g., 3x + 4 = 7), while an inequality involves "less than" or "greater than" (e.g., 3x + 4 > 7). Equations and inequalities can be used to symbolically model situations.
Studying equations and inequalities in context helps students develop a deep understanding of the meaning of both the equation or the inequality and the solution. Inherent in the study of equations and inequalities is the use of algebraic expressions, and students should understand the difference between equations and expressions. Students should distinguish between an equation and an inequality and compare and contrast their properties and the methods for solving them. They should become fluent in connecting the symbolic representation with the situation being represented. Further, the discussion about the reasonableness and meaning of the solution, if it exists, is important.
Methods for solving equations and inequalities include symbolic, numeric, and graphic. Algebraic properties for real numbers should be used fluently, with a focus on equivalent equations. One specific application of equations involves formulas that contain multiple variables. Students should be able to manipulate such formulas and develop a conceptual understanding of the meaning of the formulas through their context.
Once the concept of an equation and its solution is studied, students move to the study of systems of equations, both linear and nonlinear systems. Students will analyze different and appropriate methods for solving systems of equations (symbolically, graphically, numerically, and using matrices).