Question

x is an integer such that -x∣x∣≥4 what is the value of x?

Answer 1

The value of x is 4.

Answer 2

x ∈ (-∞, -2]

Step-by-step explanation:

For a modulus function

We know that

∣x∣ = -x   If x < 0

∣x∣ = x     If x ≥ 0

Given,

-x∣x∣≥4

Case I

x < 0

-x (-x) ≥ 4

or x² ≥ 4

or, x²-4 ≥ 0

or, (x-2)(x+2) ≥ 0

⇒ x ∈ (-∞, -2] ∪ [2, ∞)

But we have already taken x < 0

Thus,

x ∈ (-∞, -2]

Case II

x ≥ 0

-x (x) ≥ 4

or, -x² ≥ 4

or, x² + 4 ≤ 0

Which is not possible for any real x

Thus,

x ∈ (-∞, -2]

Hope this answer is helpful.

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