Find all values of t such that \($\lfloor t\rfloor = 3t + 4$\). If you find more than one value, then list the values you find in increasing order, separated by commas.

 Oct 22, 2023

The floor function rounds a number down to the nearest integer, so the equation ⌊t⌋=3t+4 means that the integer part of t is equal to 3t+4. This can happen only if t is at least −2, since the integer part of any number less than −2 is −3.

If t is at least −2, then the integer part of t is equal to t itself. Therefore, we have the equation t=3t+4. Solving for t, we get 2t=4, so t=2​.

 Oct 27, 2023

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