At Least, At Most

Many everyday phrases stand for an inequality sign. "At least 5" means 5 or more, so it is $x \ge 5$. "At most 5" means 5 or fewer, so it is $x \le 5$. "More than 5" leaves 5 out, so it is $x > 5$. "Fewer than 5" and "less than 5" also leave 5 out, so they are $x < 5$. "No more than" means the same as "at most". "No less than" means the same as "at least".

A taxi charges 3 to start and 2 per kilometre. You have at most 21 to spend. How far can you ride? Call the number of kilometres $x$. The cost of the ride is $3+2x$. "At most 21" means the cost is 21 or less, so the sign is ≤:

$$3+2x \le 21$$

$$2x \le 18$$

$$x \le 9$$

You can ride up to 9 kilometres. You build the inequality the same way you built equations from words. The only new step is choosing the sign from the phrase.