LAC 28:CXLII.1705. Algebraic Reasoning

A. Use properties of operations to generate equivalent expressions. 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with positive and negative rational coefficients to include multiple grouping symbols. 2. Understand that rewriting an expression in different forms can help reveal relationships between quantities in the context of a problem. B. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 1. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any, using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 2. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px+q=r and p(x+q)=r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. b. Solve word problems leading to inequalities of the form px+q>r, px + q ≥ r, px + q < r, or px + q ≤ r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.