The equation $|| x-1|+a|=4$ can have rea

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

The equation $|| x-1|+a|=4$ can have real solutions for x if 'a' belongs to the interval

Options:

(-∞, 4]

(-∞, -4]

(4, ∞)

[-4, 4]

Correct Answer:

(-∞, -4]

Explanation:

We have,

$|| x-1|+a|=4$

$⇒ |x-1|+a=±4$

$⇒ |x-1|=±4-a$

For real solutions, we must have

$±4-a>0$

$⇒ 4-a≥ 0$ and $-4-a≥0$

$⇒ a≤4$ and $a≤-4$

$⇒a≤-4⇒a∈(-∞, -4]$