$k$ 是一个正整数。 从 $k$ 的两倍中减去 5 得到一个奇数。

1. Translate the phrase into an expression in terms of $k$.

Twice of $k$ is $2k$.

Subtracting 5 from this gives

$2k - 5$.

1. Express the next consecutive odd number and form the inequality.

From part (a), the odd number is $2k-5$.

The next consecutive odd number is
$(2k-5)+2=2k-3.$

Their sum is greater than $16$, so
$(2k-5)+(2k-3)>16.$

2. Solve the linear inequality for $k$.

$(2k-5)+(2k-3)>16$
$4k-8>16$
$4k>24$
$k>6$

3. Use the positive integer condition to find the smallest possible larger odd number.

Since $k$ is a positive integer and $k>6$, the smallest possible value is
$k=7.$

The larger odd number is
$2k-3=2(7)-3=11.$