How to Solve for Interval with Abs and Max Functions?

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SUMMARY

The discussion focuses on solving inequalities involving the absolute value (abs) and maximum (max) functions. Participants emphasize the importance of graphing these functions to visualize the intervals where the max function switches between expressions. Understanding the behavior of the abs function in conjunction with max is crucial for determining the correct intervals. The conversation highlights the necessity of analyzing the points where the max function transitions to effectively solve the inequality.

PREREQUISITES
  • Understanding of absolute value functions
  • Familiarity with maximum functions
  • Basic graphing skills
  • Knowledge of inequalities
NEXT STEPS
  • Study the properties of absolute value functions
  • Learn about piecewise functions and their applications
  • Explore techniques for graphing inequalities
  • Investigate the behavior of max functions in different scenarios
USEFUL FOR

Mathematics students, educators, and anyone interested in solving inequalities involving advanced functions like abs and max will benefit from this discussion.

zli034
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Hi all:

The inequality here involves abs, and max functions, how to solve for the interval as show below?
attachment.php?attachmentid=58110&d=1366636107.jpg
 

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The very first thing you should probably do is draw the functions.
This will require you to think already about, for example, when the max switches from one expression to the other, and what the abs does here.
 

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