LAC 28:CXLII.2707. Reasoning with Equations and Inequalities

A. Understand solving equations as a process of reasoning and explain the reasoning. 1. Use properties of equality to justify and explain each step obtained from the previous step when solving an equation, assuming the original equation has a solution. a. Construct a viable argument to justify the solution method. B. Solve equations and inequalities in one variable. 1. Solve linear and absolute value equations and inequalities in one variable, including equations with coefficients represented by letters. 2. Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. b. Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. c. Recognize when the quadratic formula gives complex solutions and write them as "no real solution.” C. Solve systems of equations. 1. Solve systems of linear equations in two variables exactly and approximately. a. Use methods such as substitution, elimination, and graphing to solve. b. Justify a method for solving such systems. 2. Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables. D. Represent and solve equations and inequalities graphically. 1. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve, but may be a line. 2. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, piecewise linear, to include absolute value, and exponential functions. 3. Graph the solutions to a linear inequality in two variables as a half-plane, excluding the boundary in the case of a strict inequality, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.