Reintroducing Inequalities

5 min

Narrative

In this activity, students identify values that would satisfy the inequality x>1x>1. Students recall the meaning of the >> symbol and the fact that an inequality has many solutions. They also recall that 1 is not a solution to x>1x>1.

Launch

Since it may have been a while since students encountered this notation, remind them that x>1x > 1 is read “xx is greater than 1.” 

Give students 2 minutes of quiet work time followed by a whole-class discussion.

Student Task

The number line shows values of xx that make the inequality x>1x>1 true.

A number line with the numbers negative 5 through 5 indicated. An open circle is indicated at 1 and an arrow is drawn from the open circle extending to the right.

Select all the values of xx from this list that make the inequality x>1x>1 true.

  1. 3

  2. -3

  3. 700

  4. 1.05

  5. 1

Sample Response

3, 700, and 1.05

Synthesis

Ask students to share a few more solutions to x>1x>1. After each student shares, ask the class whether they agree or disagree. Emphasize that this inequality has many solutions—in fact, any value greater than 1 is a solution.

To highlight the fact that “greater than 1” does not include 1, ask:

  • “What does the open circle at 1 mean?” (It means 1 is not included.)
  • “Why isn't 1 a solution to the inequality x>1x > 1?” (1>11>1 is not a true statement because 1 is equal to 1.)
Anticipated Misconceptions

Some students may think 700 is not a solution to x>1.x > 1. Tell students that since there is an arrow at the end of the dark line, it includes all values that are greater than 1, even the ones not shown.

Standards
Building On
  • 6.EE.5·Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
  • 6.EE.B.5·Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
Building Toward
  • 7.EE.4.b·Solve word problems leading to inequalities of the form px + q &gt; r or px + q &lt; r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. <em>For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.</em>
  • 7.EE.B.4.b·Solve word problems leading to inequalities of the form <span class="math">\(px + q &gt; r\)</span> or <span class="math">\(px + q &lt; r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. \$

15 min

15 min