PRACTICE WITH THE PHRASES ‘AT LEAST’ AND ‘AT MOST’

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 $\,k\,$
$x\,\le k$
EXAMPLE:
Suppose that $\,x\,$ takes on values between $\,-3\,$ and $\,5\,$.
Then:
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Identifying Inequalities with Variables as True or False

 
 
    
(an even number, please)