Discovery Ed. Lessons 2.1, 2.2 & 2.3

Unit Objectives:

• Create equations and inequalities to represent real-world situations.
• Apply properties of equality to solve equations and justify the solution process.
• Apply properties of inequality to solve inequalities and graph their solutions.
• Solve literal equations for a given variable.
• Transform literal equations to solve real-world problems.
• Solve absolute value equations.
• Solve compound inequalities and absolute value inequalities.
• Identify equations and inequalities that have no solution or infinitely many solutions, including absolute value equations and inequalities.

New Jersey Student Learning Standards for this Unit:

• A.CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
• A.CED.A.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
• A.REI.A.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
• A.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
• A.REI.D.11: 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, absolute value, exponential, and logarithmic functions.