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

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    Question 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
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    Quote Originally Posted by Code2004 View Post
    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}
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