Review the differences among equations, expressions, and inequalities. Demonstrate with a scale how an equation balances out on both sides, and how an inequality has a set of solutions. Present a few real-world problems for your mathematicians to solve in pairs. Close by creating a game of word problems and then playing it as a class. This lesson was intended to teach your class the process of solving equations and inequalities by the substitution method.
Solving single variable inequalities is explored in this video. The example that Sal shows here contains fractions, shows the need to reverse the inequality because he multiples by a negative number during his computation, and shows the final result graphed on a number line.
In this video, a rational inequality is solved using two different techniques. This is a rather complex problem on inequalities, and it brings up some interesting considerations about rational functions. It would be appropriate for an advanced algebra student.
Combining the skills from the previous videos, particularly inequalities and absolute values, Sal works to solve several new sample problems. He encourages watching the video "over and over," which is a good piece of advice for mathematicians of any skill level.
Looking for a resource that goes beyond just graphing inequalities? Here is one that addresses the need to have learners reason and develop a deeper understanding of the solution set of systems of inequalities. This include writing inequalities, analyzing them algebraically, analyzing them graphically, and also through the use of charts. 
Taxi! Taxi! A bike taxi business seems the perfect solution for making money and getting exercise. Learners use their knowledge of representing real-word quantities with variables and constructing simple equations and inequalities to make a profit in this new business venture. The lesson also has an extension that introduces graphing and using the graphing calculator.
Delve into the hard numbers and fundamental concept of income inequality in the United States, using graphs, detailed reading materials, and an organized learning exercise.
When is the last time you assigned your students only one problem? This seemly simple problem requires learners think like a mathematician and reason about how to solve this compound inequality in one variable. More than just using skills to solve, they are required to creatively anlyze the problem. Three alternative solutions are given, each explained in clear detail. 
The outline to a lesson on setting up and solving inequalities is provided for you in this document. Step-by-step instructions that include real-world examples will lead your class to mastering this discrete skill. Consider creating a presentation and a handout with the suggested word problems in order to make them visible for learners and provide a space for them to take notes. The practice section on the third page could be used as homework or as an assessment of understanding.
Cooperative algebra learners swim from the opening pool problem through inequality-infested waters and into life-altering decisions all within one class period. Modeling a pool scenario with an inequality in one variable opens this instructional activity, which eventually ends with our swimmers modeling a job choice scenario using an inequality to decide which job is best. In between the pool and their job decision is an all-class activity delving into the consequences of operations applied to the two sides of an inequality. Then a mix-n-match game gives our swimmers practice solving inequalities in one variable and matching the solution to its graph. The cooperative debate to decide which job to take is modeled by a one variable inequality. They solve the inequality, and represent their solution set graphically and interpret their solution set within the context of the problem and make decisions based on their solution.
It all comes together in this video, in which Sal uses the concepts from his previous videos (inequalities involving adding, subtracting, multiplying, and dividing) and addresses them in several problems dealing with compound inequalities. He successfully takes a high-level, often-confusing skill and makes it easy to understand with his straightforward approach.
After defining compound inequality problems as "just inequality problems that have more than one set of constraints," Sal goes on to solve several sample problems. Those who have a hard time with multi-step equations might find this video especially informative.
Beginning a "handful of fairly simple inequality videos," Sal demonstrates a few inequality problems in which mathematicians need to add or subtract. Though he states that his goal is to familiarize viewers with the notation, his problem-solving skills are equally beneficial for even the most advanced pupils.
Things get a little more complicated in this video, which features Sal solving several inequality problems involving multiplying and dividing by positive and negative numbers. Additionally, he shows a few more kinds of notation to describe the solution set of an equality.
Here is video three of the four part series on solving compound inequalities. Sal demonstrates and expounds on the process he uses to solve a series of practice problems.
If your class struggles with graphing inequalities, or if your lecture could use some help from Sal, this video would be a great help. Sal's instruction is measured and patient, and viewers will walk away feeling more confident and successful in their graphing skills.
To reinforce the process necessary for solving multi-step inequalities, share this video with your class. Sal solves for x through a multi-step process demonstrating his experience and number know how with the audience.
Combining the skills from the previous videos, particularly inequalities and absolute values, Sal works to solve several new sample problems. He encourages watching the video "over and over," which is a good piece of advice for mathematicians of any skill level.
This is the final video in a four-part series on solving compound inequalities. Sal continues completing practice problems that show various aspects and constraints typical of compound inequalities.
Learners develop the concept of graphing inequalities. In this algebra lesson plan, students put two variable inequalities into slope intercept form. They graph inequalities by hand and solve word problem.

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