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Greatest Integer Function

If [x] is the...

Question

If [x] is the integral part of a real number x. Then, solve $[2 x] - [x + 1] = 2 x$ .

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Solution

$[2 x] - [x + 1] = 2 x => [2 x] - [x] - 1 = 2 x => [x] = 2 x + 1$
Here since $[x]$ is an integer,
Therefore $2 x + 1$ is also an integer.
And hence
$x = 2 x + 1$
$=> x = - 1$

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