### Learning Outcomes

By the end of this section, you will be able to:

- Use properties of equality to isolate variables and solve algebraic equations
- Solve equations containing absolute value
- Use the properties of equality and the distributive property to solve equations containing parentheses
- Clear fractions and decimals from equations to make them easier to solve
- Identify equations that have one solution, no solution, or an infinite number of solutions
- Recognize when a linear equation that contains absolute value does not have a solution

We begin our exploration of the coordinate plane and equations of lines with a review of the properties of equality that permit us to solve equations like [latex]x + 7 = 9[/latex]. We can just look at that equation and see that [latex]x[/latex] must be 2, since 2 is the number we add to 7 to obtain 9.

You can solve equations like these in your head quickly, but other equations are more complicated. Multi-step equations, ones that take several steps to solve, can still be simplified and solved by applying basic algebraic rules such as the multiplication and addition properties of equality.

In this section we will explore methods for solving multi-step equations that contain grouping symbols and several mathematical operations. We will also learn techniques for solving multi-step equations that contain absolute values. Finally, we will learn that some equations have no solutions, while others have an infinite number of solutions.

Warm up for this module by refreshing these important concepts and skills. As you study these review topics, recall that you can also return to Module 1 Algebra Essentials any time you need to refresh the basics.

### Recall for success

Look for red boxes like this one throughout the module. They’ll show up just in time to give helpful reminders of the math you’ll need, right where you’ll need it.