Question
Solve the inequality. Write the solution set in interval notation if possible
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Ask by Robbins Pierce. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is
Solution
Solve the equation
Solve the inequality by following steps:
Solve the inequality by following steps:
- step0: Solve the inequality by testing the values in the interval:
- step1: Find the domain:
- step2: Set the numerator and denominator of
equal to 0
- step3: Calculate:
- step4: Determine the test intervals:
- step5: Choose a value:
- step6: Test the chosen value:
- step7: Include the critical value:
- step8: The final solution is
- step9: Check if the solution is in the defined range:
- step10: Find the intersection:
The solution set for the inequalityis or in interval notation.
Therefore, the solution set is
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Simplify this solution Bonus Knowledge
To solve the inequality
-
Set the numerator to zero:
-
-
Set the denominator to zero (to find where the expression is undefined):
-
The critical points are
- Intervals to test:
, , ,
-
Testing intervals:
-
For
(e.g., ):
-
For
(e.g., ):
-
For
(e.g., ):
-
For
(e.g., ):
-
-
Include critical points:
-
gives in the numerator and satisfies the inequality . -
gives in the numerator and satisfies . -
is not included as it makes the denominator .
-
Now we compile everything together:
The solution set is
So the solution set in interval notation is
