Which one of the following is a representation (not to scale and in bold) of all
values of x satisfying the inequality 2 - 5x ≤ -
௫ିହ
ଷ on the real number
line?
Options:
(A)
(B)
(C)
(D)
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2022 Q.2)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Verbal Aptitude** (Grammar & Vocabulary) within the *General Aptitude* curriculum (1 Mark, MCQ).
**Problem Statement**:
> Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality 2 - 5x ≤ - ௫ିହ ଷ on the real number line?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of General Aptitude. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(C)** *""*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(D)** *""*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2022 (IIT Kharagpur) key.
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