Compare Quantity A and Quantity B and determine which is larger.
\[
\text{Quantity A: } x^3 - 6, \quad \text{Quantity B: } x + 1
\]
For when \( x<2 \), compare the two quantities.
\[ \text{Quantity A: } x^3 - 6, \quad \text{Quantity B: } x + 1 \] For when \( x<2 \), compare the two quantities.
Show Hint
- Quantity A is larger.
- The two quantities are equal.
- Quantity B is larger.
- Can't be determined from the information provided.
The Correct Option is C
Solution and Explanation
When \( x<2 \), we substitute values of \( x \) that are smaller than 2 into both expressions.
For \( x = 1 \), \[ \text{Quantity A: } 1^3 - 6 = -5, \quad \text{Quantity B: } 1 + 1 = 2. \]
For \( x = 0 \), \[ \text{Quantity A: } 0^3 - 6 = -6, \quad \text{Quantity B: } 0 + 1 = 1. \]
Step 2: Conclusion.
In both cases, Quantity B is larger than Quantity A. Therefore, the correct answer is (C).
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