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This document provides an educational lesson on solving absolute-value inequalities, explaining the process of rewriting these inequalities as compound inequalities. It includes examples, practice problems, and reflections to deep dive into the connections between absolute-value and compound inequalities.
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01
Identify the absolute value inequality that needs to be solved.
02
Isolate the absolute value expression on one side of the inequality.
03
Rewrite the inequality as two separate cases: one for the positive scenario and one for the negative scenario.
04
Solve each of the two inequalities separately.
05
Combine the solutions from both cases, ensuring to adhere to the original inequality sign.
06
Graph the solutions on a number line and represent them in interval notation if necessary.

Who needs solving absolute-value inequalities?

01
Students studying algebra who need to understand absolute values.
02
Professionals in fields that involve mathematical modeling or statistics.
03
Anyone preparing for standardized tests that include algebra topics.
04
Individuals needing to solve real-life problems involving distances or deviations.
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Solving absolute-value inequalities involves finding the values of a variable that satisfy an inequality containing an absolute value expression.
Typically, students or individuals working with mathematical problems that involve absolute values are required to address such inequalities, particularly in educational contexts.
To solve an absolute-value inequality, isolate the absolute value expression and then break it into two separate inequalities based on the definition of absolute value.
The purpose is to determine the range of values for a variable that makes the inequality true, which is useful in various mathematical contexts.
The solutions that satisfy the inequality must be clearly reported, often in interval notation or as a set of values.
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