Question

Number of real roots of the equation $6 x-7[x]=2$ is
[Note: $[ k ]$ denotes greatest integer function less than or equal to $k$.]

• A. 6
• B. 5
• C. 8
• D. 7

Answer 1

Answer: (A)

$6\{x\}=2+[x]$
$0 \leq\{x\}=\frac{1}{3}+\frac{[x]}{6}<1 $
$-2 \leq[x]<4 $
$\Rightarrow [x]=-2,-1,0,1,2,3 $
$\{x\}=0, \frac{1}{6}, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6}$