Interpreting The Solution To An Algebraic Inequality

Interpreting The Solution To An Algebraic Inequality

Problem-Solving Process

Opening

Problem-Solving Process

Read and Discuss

You have used a process to find solutions to real-world problems that you solve with equations or formulas. This process will also help you solve inequalities.

  • Understand the problem.
  • Represent the problem.
  • Answer the question.
  • Check that your answer makes sense.

How Many T-Shirts?

Opening

How Many T-Shirts?

Jack has $40 to spend on clothes for school. He wants to buy a pair of jeans and some T-shirts. The jeans cost $35 and the T-shirts cost $2. Jack writes this inequality to determine how many T-shirts he can buy.

35 + 2t ≤ 40

2t ≤ 5

  • Use the inequality to determine the greatest number of T-shirts Jack can buy.

Math Mission

Opening

Write inequalities to represent real-world situations, and interpret the solutions in terms of the problem situation.

Memory Cards

Work Time

Memory Cards

Marcus wants to order memory cards for his computer from an online store. If the cards cost $15.99 each, and the cost of shipping is $5.50, how many cards can he order for under $50?

  • Solve the inequality.
  • Interpret the solution to inequality.
  • Graph the solution to the problem on the number line.

HANDOUT: Memory Cards
INTERACTIVE: Graph an Inequality

Hint:

Think about what the solution to the inequality should look like based on the problem situation and question.

Water Tank

Work Time

Water Tank

A water tank contains 1,000 gallons of water. Water begins draining out of the tank at a rate of 6 gallons per minute. After a while, the tank contains less than 200 gallons of water. How long has water been draining out of the tank?

  • Solve the inequality.
  • Interpret the solution to inequality.
  • Graph the solution to the problem on the number line.

HANDOUT: Water Tank
INTERACTIVE: Graph an Inequality

Hint:

Think about what the solution to the inequality should look like based on the problem situation and question.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Choose one of the problems from the previous tasks.
  • Show all the steps to solve your inequality. Then explain how you determined the solution to the situation and how you graphed that on the number line.

Challenge Problem

  • Write an explanation of the steps you use to solve an inequality, including how to interpret the solution based on the problem situation.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about other classmates' solutions, and their interpretations of the solutions.

Hint:

As your classmates present, ask questions such as:

  • Why did you use the “less than” symbol instead of the “less than or equal to” symbol?
  • Why did you reverse the inequality sign?
  • Why didn’t you reverse the inequality sign?
  • Why isn’t “–1” a solution to the problem?

Inequalities

Formative Assessment

Summary of the Math: Inequalities

Write a summary about solving inequalities and interpreting solutions.

Hint:

Check your summary:

  • Do you explain how to graph an inequality on a number line?
  • Do you explain how to interpret a solution, and discuss the types of factors in a problem that might require you to adjust the mathematical solution to fit the problem situation?

Working With Inequalities

Formative Assessment

Working With Inequalities

Complete this Self Check by yourself.

  1. Solve the inequality (show all your steps) and represent the solution on the given number line.
           8x + 10 ≤ 66
  2. Write a word problem that could be solved using the inequality.

  3. Write a sentence that answers your word problem.

HANDOUT: Solving and Checking Inequalities
INTERACTIVE: Graphing an Inequality

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

The most important thing I learned in this lesson is...