1.8 Inequalities
Ideas in this lesson
- Test solutions and endpoint restrictions
- Solve linear inequalities
- Combine compound inequalities
- Solve polynomial inequalities with sign charts
- Solve rational inequalities and preserve exclusions
- Solve absolute-value inequalities
- Translate distance and tolerance descriptions
- Use inequalities in domains and models
- Solve parameter-dependent inequalities
- Translate and solve unit-sensitive linear models
- Analyze nonlinear physical and economic models
- Prove order properties and compare distances
Test solutions and endpoint restrictions · Worked example
A sensor accepts a reading \(r\) only when \(2\le r<6\). Which boundary decision is correct?
Answer: \(r=2\) is accepted; \(r=6\) is rejected.
The lower inequality uses an inclusive sign, so equality at the lower endpoint is allowed.
The upper inequality is strict, so equality at the upper endpoint fails.
A valid reading must satisfy both conditions at once.
The upper inequality is strict, so equality at the upper endpoint fails.
A valid reading must satisfy both conditions at once.