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Algebra 1 3-7 Guided Practice: Absolute Value Equations and Inequalities

By Matt Richardson
Last updated almost 3 years ago
17 Questions

Solve It: Serena skates toward Darius and then passes by him.


She skates at a constant speed of 20 ft/s. At what time(s) is Serena 60 ft from Darius? Select all that apply.

  • 1 second
  • 2 seconds
  • 3 seconds
  • 5 seconds
  • 6 seconds
  • 8 seconds
  • 9 seconds
  • Serena is 60 ft from Darius after...
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In the Solve It, Serena's distance from Darius decreases then increases. You can use absolute value to model such changes.

Take Note: Describe the process of solving an absolute value equation.

Problem 1 Got It? What are the solutions of the equation?

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Problem 1 Got It? Graph and check the solutions. Include relevant graph detail.
Show your work on the canvas. You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.CED.1

Take Note: Solving the two absolute value equations below algebraically requires different processes.
2|x|+3=15
|2x+3|=15
Describe how those processes are similar and how they are different.

You are not required to solve the equations, but may do so if it is helpful. You may also use the canvas to help illustrate your explanation.

Take Note: Why is it that we can expect most absolute value equations to have two solutions?

Hint: Remember that absolute value can be thought of as distance from 0 on a number line.

Problem 2 Got It? Another friend's distance d from you (in feet) after t seconds is given by d = |80 - 5t|.
What does the 5 in the equation represent?

A.SSE.1.b
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Problem 2 Got It? Another friend's distance d from you (in feet) after t seconds is given by d = |80 - 5t|.
What does the 80 in the equation represent?

A.SSE.1.b
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Problem 2 Got It? Another friend's distance d from you (in feet) after t seconds is given by d = |80 - 5t|.
At what time(s) is she 60 ft from you?
Select all that apply.

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Problem 3 Got It?
Select all that apply.
Make sure that you double check your solutions.

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A.SSE.1.b

Take Note: Let b be a real number greater than 0. Match each style of absolute value inequality graphs with the general form of an absolute value inequality that would generate them.

|x|<b
|x|\leq b
|x|>b
|x|\geq b

Problem 4 Got It? What are the solutions of the inequality?
Show your work on the canvas. You may complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

A.SSE.1.b
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Problem 4 Got It? Graph the solutions of the inequality.
Include all relevant graph detail.

A.SSE.1.b
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Problem 5 Got It? A food manufacturer makes 32-oz boxes of pasta.


Not every box weighs exactly 32 oz. The allowable difference from the ideal weight is at most 0.05 oz.
Write and solve an absolute value inequality to find the range of allowable weights.

A.SSE.1.b
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Problem 5 Got It? Reasoning: In Problem 5, could you have solved the inequality |w - 213| ≤ 5 by first adding 213 to each side?

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Problem 5 Got It? Reasoning: Explain your response to the previous item.

A.SSE.1.b
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Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?