Solve Absolute Value Inequalities Worksheet

Algebra 2
Inequalities

Total questions - 6

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How Will This Worksheet on "Solve Absolute Value Inequalities" Benefit Your Student's Learning?

  • Effectively compare absolute values.
  • Solve problems involving absolute values.
  • Explore different solutions by splitting inequalities.
  • Gain confidence in manipulating absolute values.
  • Establish a strong foundation for advanced mathematics.
  • Develop critical thinking skills by analyzing different cases of inequalities.
  • Enhance problem-solving abilities with practical examples.

How to Solve Absolute Value Inequalities?

  • Start by isolating the absolute value expression if it's not already.
  • Consider both scenarios: where the expression inside the absolute value is positive and where it is negative.
  • Solve each scenario as a separate inequality.
  • Combine the solutions obtained from both scenarios to find the complete solution to the absolute value inequality.

Solved Example

Q. Solve for u u .\newlineu46 |u| - 4 \geq 6 \newline\newlineWrite a compound inequality like 1<x<3 1 < x < 3 or like x<1 x < 1 or x>3 x > 3 . Use integers, proper fractions, or improper fractions in simplest form.\newline________
Solution:
  1. Isolate absolute value expression: We are given the inequality u46|u| - 4 \geq 6. Our first step is to isolate the absolute value expression on one side of the inequality.\newlineu4+46+4|u| - 4 + 4 \geq 6 + 4\newlineSimplifying both sides gives us:\newlineu10|u| \geq 10
  2. Consider definition of absolute value: Now that we have u10 |u| \geq 10 , we need to consider the definition of absolute value. The absolute value of u u is greater than or equal to 10 10 means that u u is either greater than or equal to 10 10 or less than or equal to 10 -10 .\newlineThis gives us two inequalities:\newlineu10 u \geq 10 or u10 u \leq -10
  3. Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality.\newlineThe compound inequality is:\newlineu10u \leq -10 or u10u \geq 10
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About Worksheet

Algebra 2
Inequalities

To solve absolute value inequalities, start by simplifying the inequality. If the absolute value of \( x \) is greater than a positive number, then \( x \) can be greater than the number or less than its negative. Mathematically, if \( |x| > a \), then \( x > a \) or \( x < -a \). Use these worksheets to enhance your understanding of absolute value.

Example: Solve the absolute value inequality \( |2x - 1| > 5 \).

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