In this chapter, we explore the idea of equality. The Properties of Equality are introduced as a way to maintain equality while manipulating equations. We use these concepts to show that solving equations can help us find the value(s) of a variable that makes an equation true.
When applying one or more of the Properties of Equality to an equation the form of the equation changes but its solution set remains the same. This allows us to use various mathematical operations, including addition, subtraction, multiplication and division, to manipulate an equation to find its solution or solutions.
The solution set of one-variable equations is the value or values the variable can have such that the statement is true. This happens only when both sides of the equation are equivalent.
To start, we will solve one-step and multi-step equations by using inverse operations, the Distributive Property, combining like terms, and dealing with variables on both sides of an equation.
Inverse operations are two operations that, without changing the solution set, undo each other.
The methods presented in the chapter will also be applied to literal equations. These are equations that have more than one variable. Finally, we create and solve one-variable equations to model and solve situations in context.