Question 10.
The largest real value of a for which the equation |x + a| + |x − 1| = 2 has an infinite number of solutions for x is
A
-1
B
0
C
1
D
2
Question Explanation
Text ExplanationVideo Explanation
In the question, it is given that the equation ∣x+a∣+∣x−1∣=2
∣x+a∣+∣x−1∣=2 has an infinite number of solutions for any value of x. This is possible when x in |x+a| and x in |x-1| cancels out.
Case 1:
x + a < 0, x - 1 ≥ 0
- a - x + x - 1 = 2
a = -3
Case 2:
x + a ≥ 0 and x - 1 < 0
x + a - x + 1 = 2
a = 1
Largest value of a is 1.
The answer is option C.
