# Math Help - Inequalities and Surds - dying of confusion over this question.

1. ## Inequalities and Surds - dying of confusion over this question.

Hi, I've been staring at this question on my 'homework' sheet for ages, and after... So long, I decided I need help. If possible, could someone solve the question and explain the process quickly please ^^!?

sqrt(2)*(x-sqrt(2)) < x+(2*sqrt(2))

Any help would be appreciated. I apologise if this is easy.

Code2004

2. Originally Posted by Code2004
Hi, I've been staring at this question on my 'homework' sheet for ages, and after... So long, I decided I need help. If possible, could someone solve the question and explain the process quickly please ^^!?

sqrt(2)*(x-sqrt(2)) < x+(2*sqrt(2))

Any help would be appreciated. I apologise if this is easy.

Code2004
$\sqrt{2} (x - \sqrt{2}) < x + 2\sqrt{2}$

$\sqrt{2} \cdot x - 2 < x + 2\sqrt{2}$

$\sqrt{2} \cdot x - x < 2 + 2\sqrt{2}$

$x(\sqrt{2} - 1) < 2(1 + \sqrt{2})$

$x < \frac{2(1+\sqrt{2})}{\sqrt{2}-1}$

3. You're a star, I love you.