Investigating Linear Expressions, Equations, and Inequalities in One Variable Overview

In this module, you will use algebraic reasoning to create, interpret, solve, and graph linear equations and inequalities, in one variable. The equations and inequalities include those with rational coefficients, variables on both sides and whose solutions require the use of the distributive property and combining like terms. You will also interpret expressions with multiple factors or terms and manipulate linear and literal equations expressed in various forms.

Essential Questions

How can we analyze connections between linear equations and use them to solve problems?
What does each part of an expression represent in the context of the problem?
How are polynomial operations related to operations in the real number system?
How can polynomials be used to express realistic situations?
How do I solve and justify my answer to an equation or inequality in one variable?

Key Terms

The following key terms will help you understand the content in this module.

Binomial Expression - An algebraic expression with two unlike terms.

Coefficient - A number multiplied by a variable in an algebraic expression.

Constant Rate of Change - With respect to the variable x of a linear function y = f(x), the constant rate of change is the slope of its graph.

Constant Term - A quantity that does not change its value.

Equation - A number sentence that contains an equal symbol.

Expression - A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Factor - For any number x, the numbers that can be evenly divided into x are called factors of x. For example, the number 20 has the factors 1, 2, 4, 5, 10, and 20.

Inequality - Any mathematical sentence that contains the symbols > (greater than), < (less than), ≤ (less than or equal to), or ≥ (greater than or equal to).

Integer - The set of numbers ..., –3, –2, –1,0,1,2,3,...

Monomial Expression - An algebraic expression with one term.

Substitution - To replace one element of a mathematical equation or expression with another.

Term - A number, a variable, or a product of numbers and variables.

Variable - A letter or symbol used to represent a number.

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