Math Problem Statement
x < 0 olduğuna göre, |5x + |2x + |-x||| ifadesinin değeri nedir?
Solution
The problem asks us to evaluate the expression under the condition that .
Step-by-step solution:
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Expression Breakdown:
- We have a nested absolute value expression. Let’s handle this layer by layer starting from the innermost absolute value.
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Innermost Absolute Value: :
- Since , is positive. Therefore, .
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Next Level Absolute Value: :
- From the previous step, , so the expression inside this absolute value becomes:
- Since , .
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Outer Absolute Value: :
- Now substitute into the outer expression:
- Again, since , .
Final Answer:
The value of the expression is .
Would you like further clarification or have any other questions? Here are some related questions for practice:
- How do absolute values work when nested within other absolute values?
- What happens if the condition was in this problem?
- Can you think of a general strategy for solving absolute value problems with variables?
- How does the result of this problem change if the coefficients are different?
- How would you represent this solution graphically on the number line?
Tip: Always simplify absolute value expressions by analyzing each layer carefully, starting from the innermost part.
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Math Problem Analysis
Mathematical Concepts
Absolute Value
Algebraic Expressions
Formulas
Absolute Value Property: |a| = a if a >= 0, |a| = -a if a < 0
Theorems
Absolute Value Theorem
Suitable Grade Level
Grades 9-11