Math Problem Statement
Absolute value of x cube plus 4 less than 5
Solution
The inequality given is:
To solve this inequality, we can interpret it as two separate inequalities since the absolute value expression implies that the expression inside can be both positive and negative.
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Split the Inequality:
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Break it into two inequalities:
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Solve each inequality separately:
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For : Taking the cube root of both sides:
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For : Taking the cube root of both sides:
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Combine the Solutions: The solution to the inequality is:
So, the solution set for is approximately:
Let me know if you’d like further explanation on any step!
Related Questions:
- How does solving an absolute value inequality differ from solving a standard inequality?
- What are the applications of absolute value inequalities in real-world contexts?
- How would the solution change if the inequality was instead?
- Could the inequality have a solution, and how would it be determined?
- What methods can be used to approximate roots like ?
Tip: When solving absolute value inequalities, always remember to split the inequality into two cases: one for the positive scenario and one for the negative scenario.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Inequalities
Cubic Functions
Formulas
|x^3 + 4| < 5
Theorems
Properties of Absolute Values
Inequality Properties
Suitable Grade Level
Grades 10-12