Math Problem Statement
−(x − 3)(x + 5) < 0
Solution
We are tasked with solving the inequality:
Step 1: Eliminate the negative sign
Distribute the negative sign into the inequality:
This becomes:
Now, we are solving the inequality:
Step 2: Find the critical points
Set each factor to zero to find the critical points:
These critical points, and , divide the number line into three intervals:
Step 3: Test the intervals
We will test points from each interval to determine where the inequality holds true.
- Test point in , say :
- Test point in , say :
- Test point in , say :
Step 4: Conclusion
The inequality holds where , which is in the intervals:
Thus, the solution to the inequality is:
Do you need more details or have any questions?
Here are 5 related questions for practice:
- Solve .
- Solve .
- Solve .
- Solve .
- Solve .
Tip: When solving inequalities, always test points from each interval to determine where the inequality holds.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Quadratic Expressions
Critical Points
Intervals
Formulas
Factoring and solving quadratic expressions
Inequality testing through interval analysis
Theorems
Sign analysis of products in intervals
Critical points theorem for inequalities
Suitable Grade Level
Grades 9-11