At Least, At Most

Many everyday phrases stand for an inequality sign. "At least 5" means 5 or more, so it is x >= 5. "At most 5" means 5 or fewer, so it is x <= 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 <= 21

2x <= 18

x <= 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.