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in Linear Equations by (15.2k points)

Solve |x| > 4, when x ϵ R.

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1 Answer

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by (15.7k points)

x| > 4 Square 

⇒ x 2 > 16 

⇒ x 2 – 16 > 0 

⇒ x 2 – 4 2 > 0 

⇒ (x + 4)(x – 4) > 0 

Observe that when x is greater than 4, (x + 4)(x – 4) is positive 

And for each root the sign changes hence

We want greater than 0 that is positive part 

Hence x should be less than -4 and greater than 4 for (x + 4)(x – 4) to be positive 

x less than -4 means x is from negative infinity to -4 and x greater than 4 means x is from 4 to infinity 

Hence x ∈ (-∞, -4) and x ∈ (4, ∞) 

Hence the solution set of |x| > 4 is (-∞, -4) U (4, ∞)

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