Interpreting Inequalities

Party Decorations

5 min

Problem

Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

  1. ​Andre wrote the inequality 3x+10≤303x + 10 \leq 30 to plan his time. Describe how this inequality represents the situation.

  2. Solve Andre’s inequality, and explain what the solution means.

Answer

  1. Sample response: The variable xx represents the number of small paper cranes Andre can make. 3x3x is the amount of time it takes to make xx small cranes. 10 is the number of minutes it takes to make the centerpiece. 30 is Andre’s time limit in minutes.
  2. x≤623x \leq 6\frac23. Sample response: Andre can make up to 6 small cranes.​

Sample Response

  1. Sample response: The variable xx represents the number of small paper cranes Andre can make. 3x3x is the amount of time it takes to make xx small cranes. 10 is the number of minutes it takes to make the centerpiece. 30 is Andre’s time limit in minutes.
  2. x≤623x \leq 6\frac23. Sample response: Andre can make up to 6 small cranes.​
Responding to Student Thinking
Points to Emphasizepoints_to_emphasize

Response: If students struggle with interpreting the inequality or its solution, plan to review this concept when opportunities arise over the next several lessons. For example, make sure to invite multiple students to share their thinking about how the inequalities represent the situations in this activity:

Standards
Addressing
  • 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. \$