LAC 28:CXLII.2513. 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. Expand context to situations, including but not limited to logarithmic, exponential, rational, and radical equations. a. Construct a viable argument to justify the solution method. 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. B. Solve equations and inequalities in one variable, including applications in mathematical modeling. 1. Solve quadratic equations in one variable by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Apply these methods to represent and solve real-world problems through mathematical modeling, interpreting the meaning of solutions in context. C. Solve systems of equations. 1. Solve systems of linear equations exactly and approximately, limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables. 2. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. D. Represent and solve equations and inequalities graphically. 1. 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 approximate solutions by using technology to graph functions, make tables of values, or find successive approximations. Including cases where f(x) and/or g(x) are polynomial, rational, absolute value, exponential, and logarithmic functions.