IA1.AT.B: Make sense of and solve equations, inequalities, and systems of equations or inequalities.

Make sense of and solve equations, inequalities, and systems of equations or inequalities.

IA1.AT.B.2Create and solve one-variable equations, justify the solution process, and interpret the solution(s) in context. a. Create linear and exponential equations in one variable to represent relationships between quantities. b. Solve linear equations in one variable using flexible and efficient strategies. Justify the solution process using logical steps and explanations. Interpret the meaning of the solution in context. c. Solve absolute value equations in one variable where the absolute value expression is isolated on one side of the equation. Justify the solution process and interpret the solution(s) in context. d. Solve exponential equations where both sides have comparable exponential expressions, requiring at most two steps to rewrite expressions to the same base, and explain the reasoning using properties of exponents.IA1.AT.B.3Create and solve one-variable inequalities, justify the solution process, and interpret the solutions in context. a. Create inequalities in one variable to represent constraints or conditions. b. Solve linear inequalities in one variable, including those with variables on both sides, using flexible and efficient strategies. Represent the solution set using a number line and inequality notation. c. Solve absolute value inequalities in one variable where the absolute value expression is isolated on one side of the inequality. Represent the solution set using compound inequalities and a number line. d. Interpret the meaning of the solution set in the context of the problem, including what values are reasonable within the given situation.IA1.AT.B.4Create linear and exponential equations in two variables, graph them, and use those graphs to represent and solve problems in context. a. Create linear and exponential equations in two variables to model relationships, and graph them on the coordinate plane. b. Use the understanding that the graph of an equation represents the set of all its solutions to identify solutions, describe patterns, and interpret the relationship between variables.IA1.AT.B.5Create, solve, and analyze systems of two linear equations in two variables in context. a. Create systems of linear equations to represent relationships. b. Solve systems of linear equations using algebraic methods (i.e., substitution and linear combination). c. Approximate or verify solutions to systems of equations by graphing and identifying the point of intersection. d. Interpret the meaning of the solution in context.IA1.AT.B.6Create linear inequalities in two variables to represent constraints in context and graph the solution set as a half-plane within the coordinate plane.IA1.AT.B.7Represent and analyze systems of two linear inequalities in two variables in context. a. Create systems of linear inequalities in two variables to represent constraints and relationships. b. Graph the solution set to a system of linear inequalities as the intersection of the corresponding half-planes. c. Interpret the meaning of the solution set in context and determine whether given ordered pairs are solutions to the system.IA1.AT.B.8Model and solve optimization problems using systems of linear inequalities. a. Represent contexts involving constraints and an objective to optimize (i.e., maximize or minimize) using a system of linear inequalities. b. Graph the feasible region and identify solutions that satisfy all constraints. c. Identify and justify the optimal solution(s) based on the objective, and interpret the meaning in context.IA1.AT.B.9Use technology to solve systems of equations consisting of a linear equation and an exponential in two variables and interpret the solution within a given context.

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