# Solve Absolute Value Inequalities Worksheet

## 6 problems

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 $$|2x - 1| > 5$$.

Algebra 2
Inequalities

## 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 $u$.$\newline$$|u| - 4 \geq 6$$\newline$$\newline$Write a compound inequality like $1 < x < 3$ or like $x < 1$ or $x > 3$. Use integers, proper fractions, or improper fractions in simplest form.$\newline$________
Solution:
1. Isolate absolute value expression: We are given the inequality $|u| - 4 \geq 6$. Our first step is to isolate the absolute value expression on one side of the inequality.$\newline$$|u| - 4 + 4 \geq 6 + 4$$\newline$Simplifying both sides gives us:$\newline$$|u| \geq 10$
2. Consider definition of absolute value: Now that we have $|u| \geq 10$, 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 $-10$.$\newline$This gives us two inequalities:$\newline$$u \geq 10$ or $u \leq -10$
3. Write compound inequality: We can now write the compound inequality that represents the solution to the original inequality.$\newline$The compound inequality is:$\newline$$u \leq -10$ or $u \geq 10$

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”