# OCR A Level: Core 3 - Modulus [January 2013 Q3]

Algebra Level 3

$$(\textbf{a})$$ Given that $$|t|=3$$, find the possible values of $$|2t-1|$$.

$$(\textbf{b})$$ Solve the inequality $$|x-\sqrt2|>|x+3\sqrt2|$$.

Let the two possible values of $$|2t-1|$$ be $$y$$ and $$z$$, and let $$x_{min}$$ be the minimum value that $$x$$ does not satisfy.

Input $$x_{min}^2+y+z$$ as your answer.

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