How to Solve Integers Inequalities involving Absolute Values?
This easy-to-follow guide will teach you more about integer inequalities involving absolute values.
![How to Solve Integers Inequalities involving Absolute Values?](https://www.effortlessmath.com/wp-content/uploads/2023/01/Solving-Integers-Inequalities-involving-Absolute-Values-512x240.jpg)
A step-by-step guide to solving inequalities involving absolute values
An absolute value is the distance between zero and a number. An example of absolute value would be \(|5|\). This shows it’s five spaces from \(0\). Therefore, the absolute value of it is also \(5\).
Solving inequalities involving absolute values can be done in the following steps:
- Isolate the absolute value expression on one side of the inequality: Start by subtracting or adding the same value on both sides so that the absolute value expression is on its own on one side of the inequality.
- Split the inequality into two cases: Once the absolute value expression is isolated, split the inequality into two cases, one where the expression inside the absolute value is positive and one where it is negative.
- Solve for each case: Solve for the positive and negative cases separately. If the expression inside the absolute value is positive, then the inequality remains unchanged. If it’s negative, then reverse the direction of the inequality.
- Combine the solutions: The solutions from the two cases are combined to form the final solution. This will be the range of values that satisfy the inequality involving absolute values.
Integers inequalities involving absolute values – Example 1
Compare the absolute value of the numbers: \(|-6|,|3|\)
Solution:
Step 1: Simplify the absolute value. \(|-6|=6\) and \(|3|=3\)
Step 2: Now decide which number is greatest, least, or equal.
\(6>3\)
Integers inequalities involving absolute values – Example 2
Compare the absolute value of the numbers: \(|-2|,|2|\)
Solution:
Step 1: Simplify the absolute value. \(|-2|=2\) and \(|2|=2\)
Step 2: Now decide which number is greatest, least, or equal.
\(2=2\)
Exercises for integers inequalities involving absolute values
Compare the absolute value of the numbers.
- \(\color{blue}{\left|-7\right|,\:\left|-9\right|}\)
- \(\color{blue}{\left|-15\right|,\:\left|15\right|}\)
- \(\color{blue}{\left|2+8\right|,\:\left|10\right|\:\:\:}\)
![](https://www.effortlessmath.com/wp-content/uploads/2023/01/image-4.png)
- \(\color{blue}{\:9>7}\)
- \(\color{blue}{15=15}\)
- \(\color{blue}{10=10}\)
Related to This Article
More math articles
- How to Use Area Models to Add Fractions with Like Denominators
- How to Graph Transformation on the Coordinate Plane: Dilation?
- Understanding Trigonometry: How to Calculate the Area of Triangles
- How long is the SAT Test?
- 4th Grade PARCC Math Worksheets: FREE & Printable
- Top 10 Tips You MUST Know to Retake the HiSET Math
- Stretching the Line: How to Multiply Fractions by Whole Numbers with Number Lines
- 4th Grade PSSA Math FREE Sample Practice Questions
- ASVAB Math Practice Test Questions
- Full-Length SAT Math Practice Test
What people say about "How to Solve Integers Inequalities involving Absolute Values? - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.