A-CED: Creating Equations and Inequalities

Creating Equations and Inequalities

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Creating Equations and Inequalities focuses on translating real-world and mathematical contexts into equations and inequalities in one or more variables. Work spans linear, quadratic, rational, and exponential forms, with attention to appropriate constraints and units. Graphs, tables, and algebraic manipulation all serve as tools for solving and interpreting these models.

A-CED.1Create 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.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A-CED.3Represent 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 cost constraints in various situations.A-CED.4Rearrange formulas (literal equations) to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
Example Problems
Solve for x.
Graph:
Tony is 5 years older than Beth. He is also 8 years older than half of Beth's age.

Let
be Tony's age and be Beth's age.

Write a system of equations to represent this situation.
Solve the equation for w:
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