2.9.9 Lesson Summary

• In this lesson, you learned how to:
• Graph the solution to an inequality in one variable.
• Solve one-variable inequalities.
• Interpret the solutions to one-variable inequalities in terms of the situation.

Here are the activities that helped you reach those goals:

• 2.9.1: Writing Solutions to Inequalities
  • In this activity, you activated what you know about the solutions to an inequality and ways to find the solutions. For the first time, you referred to the solutions as the solution set of the inequality.
• 2.9.2: Graphing Inequalities
  • In this activity, you learned how to graph an inequality on a number line. You learned how to represent an inequality using set notation. You know that an open circle is used to represent $<$ and $>$, while a closed circle represents $\le$ and $\ge$.
• 2.9.3: Understanding the Meaning of an Inequality
  • In this activity, you interpreted an inequality and its solution set in terms of a situation. Adding context can help you intuit why the solutions to an inequality are often represented by a ray on the number line. The activity also prompted you to think about the solutions to an inequality in terms of a related equation.
  • 2.9.3: Self Check
  • 2.9.3: Additional Resources
• 2.9.4: Making Sense of Inequalities and Their Solutions
  • In this activity, you received another opportunity to make sense of inequalities and their solutions in context. The context helped reinforce why it makes sense for the solutions to an inequality to be represented by a set of points on one side of a particular value on the number line.
• 2.9.5: Comparing Equality and Inequality
• • In this activity, you further developed the idea that we can solve an inequality by first solving a related equation. Previously, you reasoned about the solutions to an inequality in context. Here, you transitioned to solving an inequality without a context.
  • 2.9.5: Self Check
  • 2.9.3: Additional Resources
• 2.9.6: Using Technology to Visualize Inequality Solutions
  • In this activity, you visualized an inequality in one variable in another way: by graphing the expressions on each side and comparing the values of the expressions at different values of the variable. This allows you to see the values at which the inequality is satisfied.
• 2.9.7: Identifying Inequality Solutions on a Graph
  • In this activity, you identified a graph that correctly showed the solution to an inequality.

After these activities, you completed the following practice:

• 2.9.8: Practice