Introduction to Solving Equations Using the Properties of Equality

What you will learn to do: Solve single- and multi-step linear equations.

Writing and solving algebraic equations is an important part of mathematics. Equations can be used to describe economic, cultural, physical, and biological processes. They help business people make decisions, and help doctors and scientists find ways to heal and help people. Without mathematical equations, we would not have the physical infrastructure that we rely on every day for transportation and clean water.

Equations can help you model situations and solve problems in which quantities are unknown (like how long Joan should wait before she drives home). The simplest type of algebraic equation is a linear equation that has just one variable.

When you follow the steps to solve an equation, you try to isolate the variable. The variable is a quantity we don’t know yet. You have a solution when you get the equation [latex]x[/latex] = some value.

A platter of various sliced meats, cheeses, and bread on a table with a candle in the middle of it, and a wine glass and silverware nearby.

A dinner with friends often ends with a math problem.

While out for dinner with your friends, you decide to share a few appetizers. At the end of the meal, you want to split the bill evenly among the four of you. How much should each person pay? In this chapter, you’ll learn how to solve equations using the Division and Multiplication Properties of Equality, so you and your friends can accurately divide the bill.

Before you get started in this module, try a few practice problems and review prior concepts.


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