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.u46Write a compound inequality like 1<x<3 or like x<1 or x>3. Use integers, proper fractions, or improper fractions in simplest form.________
Solution:
  1. Isolate absolute value expression: We are given the inequality u46. Our first step is to isolate the absolute value expression on one side of the inequality.u4+46+4Simplifying both sides gives us:u10
  2. Consider definition of absolute value: Now that we have u10, we need to consider the definition of absolute value. The absolute value of u is greater than or equal to 10 means that u is either greater than or equal to 10 or less than or equal to 10.This gives us two inequalities:u10 or u10
  3. Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality.The compound inequality is:u10 or u10
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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 |2x1|>5.

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