The sentence ‘$\,x\,$ is at least $\,5\,$’ means that the least
$\,x\,$ is allowed to be is $\,5\,$;
it can be $\,5\,$, or any number greater than $\,5\,$.
So, the phrase ‘$\,x\,$ is at least $\,5\,$’ means
‘$\,x\ge 5\,$’.
The sentence ‘$\,x\,$ is at most $\,10\,$’ means that the most
$\,x\,$ is allowed to be is $\,10\,$;
it can be $\,10\,$, or any number less than $\,10\,$.
So, the phrase ‘$\,x\,$ is at most $\,10\,$’ means
‘$\,x\le 10\,$’.
More generally:
sentence | meaning of sentence | equivalent sentence |
$x\,$ is at least $\,k$ | the least
$\,x\,$ is allowed to be is $\,k\,$; it can be $\,k\,$ or any number greater than $\,k\,$ |
$x\,\ge k$ |
$x\,$ is at most $\,k$ | the most
$\,x\,$ is allowed to be is $\,k\,$; it can be $\,k\,$ or any number less than $\,k\,$ |
$x\,\le k$ |