Solving Linear Inequalities

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SWBAT solve linear inequalities and represent their solution on a number line.

Big Idea

Students will apply their knowledge of multi-step equations to solve linear inequalities.

Do Now

10 minutes

Today's Do Now will take about 5 minutes. My students are asked to order a set of numbers from least to greatest. The majority of my students can easily complete this activity , but some may struggle to remember place value. As a visual aid, my students can use the number line diagram on the top of their paper. 

After 5 minutes, we will review the answers as a whole group. I will model the answers with a number line, as students call out their responses aloud. Graphing on and reading from number lines will be used heavily throughout this unit, so it is important to review this exercise in its entirety. 

Next, a student volunteer will read today's objective, "SWBAT solve linear inequalities and represent their solution on a number line." I will ask students to define inequality, both in a real life sense, and, in mathematics.



15 minutes

During this section of the lesson, I ask my students to complete a sorting activity. The task gets students thinking about the truth value of a statement as we begin this unit on solving inequalities. The class will have 5 minutes to sort the cards into two separate piles, one for true statements and one for false statements. We will then review statements on the cards aloud.


Teacher Note: The cards for the true false sort must be cut out before class begins.

Guided Notes + Practice

25 minutes

As we move from numerical examples into algebraic expressions, students will follow along at their seats using these Guided Notes and this Presentation.

Slide 3: I will ask students to call out all of the speeds that can be driven on this road, without the risk of a speeding ticket. As students call out speeds, I will write them on the screen. I will then summarize all of our answers by writing x ≤ 40. I will ask students it they agree or disagree with the inequality that I created using a thumb up or a thumb down.

Slide 4: Next I will ask students to call out heights of people that would be allowed to board this ride. I will again record the values that students call out on the board, and then summarize these responses as x ≥ 54.

Slide 6: Students will write the corresponding inequality symbol below its name. Students will also record which inequalities should be represented on a number line with an open circle, and which should be represented with a closed circle. We will then discuss the relationship between the the shading of a circle with its actual meaning.

I will then give the class a few minutes to graph the 4 inequalities on bottom of their Guided Notes. Many students will incorrectly graph the inequality symbols by simply drawing the arrow the same direction as the inequality sign. To combat this, I will ask students to use test points to verify that their shading is correct.

Slide 6: We will solve these four problems, highlighting their similarities and differences. For the two inequality problems, I will ask students to populate a list of different solutions that would keep the the inequality true.

I will tell students to solve the inequalities on Slide 9 independently, but to check their answer with a test point. Students will realize that two of their solution sets are incorrect, even though they have not made any errors while solving. I will ask students to examine the four problems, and to find a similarity between the two problems with incorrect solution sets. This will lead students to the Main Idea prompt on their notes:

To keep a true statement when solving an inequality with the multiplication of a negative number and the division of a negative number, you must reverse the inequality.

Partner Practice: Versatiles

20 minutes

Students will practice solving linear inequalities using the ETA Hand to Mind Versatiles. Students will match correct responses to the numbered tiles in the black VersaTile case. If you do not have a VersaTiles classroom set, the assignment can still be completed by having students match questions and responses with pencil and paper.


10 minutes

As we close, I will ask students to Turn and Talk with a neighbor to decide if the solution of a linear inequality is the same as a linear equations with infinite solutions. 

Students will then complete an Exit Card.