Math Problem Statement
(x-1)(x+1)>0
Solution
To solve the inequality:
This is a quadratic inequality. Follow these steps:
Step 1: Find the critical points
The critical points are the values of that make each factor equal to 0. Set each factor to 0 and solve:
So, the critical points are and .
Step 2: Test the intervals
These critical points divide the number line into three intervals:
Now, test a value from each interval to see where the inequality holds.
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Interval : Choose .
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Interval : Choose .
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Interval : Choose .
Step 3: Exclude the critical points
Since the inequality is strictly greater than 0 (i.e., , not ), the critical points and are not included in the solution.
Final Answer:
The solution is:
This means can be any value less than or greater than , but not equal to or .
Would you like further clarification on any steps?
Here are 5 related questions for further practice:
- Solve ( (x - 2)(x + 2)
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Inequalities
Factoring
Formulas
(x - a)(x + b) > 0
Critical Points
Theorems
Sign Test for Inequalities
Factoring Method
Suitable Grade Level
Grades 9-10