The purpose of this activity is to review how the distributive property can be used as one method for solving an equation of the form , where , , or is the only variable.

This activity uses the Worked Example routine. In this routine, students analyze steps used to solve a problem and discuss specific steps with a partner and the whole class. During the discussions, students construct viable arguments to justify the steps taken by the problem solver (MP3). Later, students can apply these strategies to solve similar problems.

The purpose of this discussion is to focus on one method of solving an equation for a variable.

Tell students to open their books or devices. Display the following questions, and give students 1–2 minutes of quiet think time to consider their responses.

• “In Step 1, why did the parentheses go away?” (The negative sign outside of the parentheses indicated that everything inside of the parentheses needed to be multiplied by -1. In the first step, the solver distributed the -1 to each part inside the parentheses, so the parentheses were no longer needed.)
• “In the original equation, 7 is subtracted from . In Step 2, the solver subtracted 7 from each side of the equation. Why didn’t they add 7?” (When the solver distributed -1 to each part inside the parentheses, the operation changed from subtracting 7 to adding 7, since the product of two negative numbers is a positive number. Then, to solve for , the solver subtracted 7 from each side of the equation.)
• “In the last step, the solver did not show the math they did to get their final answer. What did they do?” (The solver divided each side of the equation by -3. This isolated on one side of the equation, which made the other side of the equation the value of .)

Ask partners to compare their responses to each question and decide if either or both answers are correct. During this partner discussion, monitor to select groups who reason about the questions in different ways. Follow with a whole-class discussion, inviting 1–2 selected groups to share their answers for each question.

If time allows, consider displaying a second worked example next to the first that either:

• Shows a different method of solving a similar problem that students can compare and contrast with the first example (MP7). For example, begin by dividing each side of the equation by -1, rather than distributing.
• Shows the same method with an error that students can critique and correct (MP3). For example, distribute the -1 to only one part inside the parentheses.

The purpose of this activity is for students to solve equations involving absolute value. This prepares students for the associated Algebra 1 lesson, where students will solve absolute value equations written as piecewise functions by rewriting the equations case by case before solving. In this activity, students solve equations with one or two solutions, depending on if the variable is in the absolute value. Students look for and express regularity in repeated reasoning (MP8) when they generalize if an equation will have one or two solutions.

In this activity, students continue solving equations involving absolute value. Students work with a partner to improve their reasoning of absolute value’s effect on an equation’s solutions.

When students articulate their reasoning, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6). They might first propose less formal or imprecise language, and after sharing with a partner, revise their explanation to be clearer and stronger.