Math Problem Statement
Simplify the expression \(\frac{\|x - 1\| - \|-2y\|}{\|3y + 2x\|}\).
Solution
The expression you uploaded is:
This expression involves absolute values. Let's break it down:
Numerator:
- is the absolute value of .
- because the absolute value of is .
So the numerator simplifies to:
Denominator:
- remains as is because it is the absolute value of the linear combination .
Thus, the entire expression simplifies to:
Let me know if you need further simplifications or details, and feel free to ask any clarifying questions!
Here are five related questions that might expand on this:
- How do you solve equations involving absolute values?
- What is the geometric interpretation of absolute value functions?
- How do we handle cases when the expression inside an absolute value equals zero?
- Can you graph this function to understand its behavior?
- How do absolute values affect the domain and range of this expression?
Tip: When simplifying absolute value expressions, consider the sign of the terms inside the absolute values, as they could affect the overall result!
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Math Problem Analysis
Mathematical Concepts
Absolute Values
Linear Expressions
Simplification
Formulas
|a|, |b| for absolute values
|-a| = |a|
Theorems
Properties of Absolute Value
Suitable Grade Level
Grades 8-10