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:-

$\sf \longmapsto \: x = \pm \: \sqrt{36}$

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