So Many Options: Solving One-Step Inequalities

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SWBAT solve one-step inequalities while demonstrating their knowledge that the solution is more than one quantity.

Big Idea

The Possibilities Are Unlimited.... Almost: Understanding when solving one-step inequalities that your solution will be many possibilities.

Curriculum Reinforcer

5 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.


5 minutes

In today's opening exercise, I will show my students 11 yellow counters and 7 red counters. Then I will ask my students the following questions:

  • What inequality can you write that compares the number of yellow counters to the number of red counters? 
  • Suppose you add 2 yellow and 2 red counters to the group. What new inequality can you write that compares the number of yellow counters to the number of red counters? 
  • What effect does adding the same value to each side have on an inequality? 
  • What if I subtract the same number of counters from both sides?
  • Will the same be true with multiplication and division?


Instruction & Teacher Modeling

10 minutes
In today's instructional piece, I will show students, using the opening exercise, how solving one-step inequalities is similar to solving one-step equations. Therefore, we can use the same method to arrive at the correct solution when solving for a variable.


During instruction, I will ensure to place emphasis on the following; 

  • When solving an inequality, the inequality remains true . . .

    • if the same number is added to or subtracted from each side of an inequality.
    • if both sides of an inequality are multiplied or divided by the same positive number.


To help my student to understand how inequalities are used mathematically, I will use the following:

    1. Is 6 + 2 < 9? yes
    2. Is 7 + 2 < 9? no
    3. Is 8 + 2 < 9? no
    4. Of the numbers 3, 4, or 5, which is a solution of the inequality m + 9 > 13? 5
    5. a + 6 < 12, a = 5? yes
    6. 18 < 21 − bb = 4 no
    7. 15 > 32 − cc = 9 no
    8. A state park recorded the number of cars entering the park on certain days last week. On which days did more than 65 cars enter the park? Use the inequality c > 65, where represents the number of cars, to solve. Wednesday


Number of Cars








The first three problems are simply to allow the students to see how an expression on one side of an inequality symbol can be compared to a quantity on the other side of that same inequality symbol.

The rest of the problems are for the purpose of determining if a given quantity makes an inequality true.

Having the students to go over and explain these types of problems will help them to grasp the concept of solving one-step inequalities.

After ensuring that the students have understood the concept of inequalities as it pertains to expressions being compared to quantities. I will then model how to solve one-step inequalities using the following:


  • Solve n + 2 > 8. Graph the solution on a number line.  ANSWER: n > 6
  • Solve y − 3 ≤ 4. Graph the solution on a number line.  ANSWER: y ≤ 7
  • Solve 3x < 21. Graph the solution on a number line.  ANSWER: x < 7
  • Rami is taking 3 of his friends to a baseball game. He has no more than $24 to spend on snacks. Write and solve an inequality to find the most he can spend on snacks for each of them. ANSWER: 4s ≤ 24; s ≤ 6




Try It Out

10 minutes

During today's guided practice, I will have my students complete the attached worksheet. I will provide them with 7 minutes to complete the problems and then I will give them the solutions to check for accuracy before we move on to the independent practice piece.

Independent Exploration

20 minutes

In today's independent practice portion of this lesson, my students will complete a task entitled, "When Is it Not Equal?" This task comes from During this task my students will practice solving for variables of a one-step inequality and graphing that solution. Before doing so, they will review what an inequality is, how to write inequalities when given phrases, and how to graph inequalities.

Closing Summary

20 minutes

To close out today's lesson,  the students will trade papers so that we can grade the worksheets and provide students with immediate feedback as to their performance on today's assignment.

Afterward, students will write the steps to solving and graphing the following inequality as a ticket out the door:

3n > 72