Math Problem Statement
Absolute value of x raised to the power of 2 +4 less than 5
Solution
To solve the inequality:
Step-by-Step Solution:
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Simplify the inequality: Since , we rewrite the inequality as:
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Isolate : Subtract 4 from both sides:
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Solve for : Take the square root of both sides. Remember that when you take the square root of both sides of an inequality, you must consider both the positive and negative roots:
Solution:
The solution to the inequality is:
This means that must be between and (not including and ) for the inequality to hold.
Would you like a more detailed explanation, or do you have any questions?
Related Questions:
- How do absolute values affect inequalities differently from normal expressions?
- What changes if the inequality symbol is instead of ?
- How would you solve ?
- What if the inequality was ?
- How do you graph solutions to inequalities like this one?
Tip: Always remember to consider both positive and negative solutions when solving inequalities involving squares and square roots.
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Math Problem Analysis
Mathematical Concepts
Absolute Value
Inequalities
Quadratic Expressions
Formulas
|x|^2 = x^2
Theorems
Properties of Absolute Values in Inequalities
Suitable Grade Level
Grades 8-10