What is the set of values of x satisfying x+1= 32 (mod 7) ?

The correct answer is option (4) : $x=...., 10, 17, 24, 31, 38, 45, 52, ............$

$x+1=32(mod\, 7)$

$x+1-32$ is divisible by 7

$x-31 $ is a multiple of 7

$x-31=7\lambda , λ∈I$

$x=31+7\lambda $

Putting $\lambda = ....., -3, -2, -1, 0 , 1, 2, 3, ......$ we get

$x=...., 10, 17, 24, 31, 38, 45, 52, ............$