Question

Which inequality represents the solution to (picture provided)

Answer 1

Question:-

`x^2-16\ge 20`

We need to solve the inequality.

Solution:-

`\sf \longmapsto \: x^2-16\ge 20`

We need to exchange ≥ to equal ( = )sign to solve Further.

`\sf \longmapsto \: x {}^(2) - 16 = 20`

Add 16 to both sides of this equation :-

`\sf \longmapsto \: x^2 - 16+16=20+16`

On Simplification of this equation:-

`\sf \longmapsto {x}^(2) = 20 + 16`

`\sf \longmapsto {x}^(2) = 36`

Then Take the square root of 36:-

`\sf \longmapsto \: x = \pm \: √(36)`

On Simplification :-

`\sf \longmapsto \: x = 6 \: or \:x = - 6`

Then,

Check the interim in between two points.

So for this, Replace x = 6 to x ≥ 6 and x = -6 to x ≤ - 6.This is the solution of this question.

`\sf \longmapsto \: x \le - 6`

And,

`\sf \longmapsto \: x \ge \: 6`

Option D

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Henceforth,The Answer is :-

`\boxed{x \: \le - 6}`

`\boxed{x \ge \: 6 }`

Option D is the correct answer

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I hope this helps!

Please let me know if you have any questions.

~MisterBrian