Digital SATMath: Advanced MathMedium
A quality control engineer is inspecting a component. The acceptable length L (in millimeters) of the component must satisfy the inequality |L - 10| ≥ 0.2. Which of the following represents the range of acceptable lengths for the component?
- AL ≤ 10.2
- BL ≥ 9.8
- CL ≤ 9.8 or L ≥ 10.2
- D9.8 ≤ L ≤ 10.2
Show answer & explanationAnswer & explanation
Correct answer: C. L ≤ 9.8 or L ≥ 10.2
The inequality |L - 10| ≥ 0.2 can be split into two separate inequalities: L - 10 ≥ 0.2 or L - 10 ≤ -0.2. Solving the first gives L ≥ 10.2. Solving the second gives L ≤ 9.8. Combining these, the acceptable lengths are L ≤ 9.8 or L ≥ 10.2.
Why the other options are wrong
- A. This only represents one part of the inequality, and it's not the correct upper bound.
- B. This only represents one part of the inequality, and it's not the correct lower bound.
- D. This is the solution for |L - 10| < 0.2, not |L - 10| ≥ 0.2.
Solving Absolute Value Inequalities (Greater Than)
An inequality of the form |x| > a (where a > 0) is equivalent to x > a or x < -a, representing values outside a certain range.
- Transforms into two separate 'or' inequalities.
- The solution set is two disjoint intervals.
- Often represents values outside a tolerance or unacceptable range.
Memory trick: Greater than, outside the bounds, two solutions are found.