Math Problem Statement
Solution
The image contains the inequality:
This is an absolute value inequality, which can be solved by considering the two cases for the absolute value expression:
Let's solve these step by step.
Case 1:
Add 1 to both sides:
Now divide by 2:
Case 2:
Add 1 to both sides:
Now divide by 2:
Final Solution:
Combining the results of both cases, the solution to the inequality is:
Thus, the solution set is .
Would you like further details or clarifications on any part of the solution?
Here are 5 related questions to deepen your understanding:
- How do you solve absolute value inequalities that involve a greater-than sign (e.g., )?
- How would you solve an absolute value inequality if it had both variables inside the absolute value?
- What is the geometric meaning of absolute value inequalities on a number line?
- Can you convert the solution of an absolute value inequality into interval notation?
- How would the inequality change if the constant on the right side was negative?
Tip: When solving absolute value inequalities, always break it down into two cases—one for the positive expression and one for the negative expression.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Inequalities
Linear Inequalities
Formulas
|a| < b means -b < a < b
Theorems
Properties of Absolute Values
Suitable Grade Level
Grades 8-10