The number of solution of $|[x] – 2x| = 4$, where [*] denotes the greatest integer ≤ x, is
Answer & explanation
Correct answer: option 2
$|[x] – 2x| = 4 ⇒ |[x] – 2([x] + \{x\})| = 4$
$⇒ |[x] + 2 \{x\}| = 4$
Which is possible only when $2\{x\} = 0,1$.
If $\{x\} = 0$, then $[x]=±4$ and then $x = –4, 4$
and if $\{x\} =\frac{1}{2}$, then $[x] + 1 = ±4$
$⇒[x] = 3, –5 ∴ x = 3 +\frac{1}{2}$ and $–5 +\frac{1}{2}$
$⇒x = 7/2, –9/2$ Hence, $x=–4, –9/2, 7/2, 4$