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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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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.