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UKMT Hamilton Olympiad, 2020

Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

We write $\lfloor x \rfloor$ to represent the largest integer less than or equal to $x$ . So, for example, $\lfloor 1.7 \rfloor = 1$ , $\lfloor 2 \rfloor = 2$ , $\lfloor \pi \rfloor = 3$ and $\lfloor -0.4 \rfloor = -1$ .

Find all real values of $x$ such that $\lfloor 3x + 4 \rfloor = \lfloor 5x - 1 \rfloor$ .

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