Idea 23of 23Builds onGraph the solutions
An inequality in a story
How do you write a real limit as an inequality?
Today you'll discover
- which sign “at most” needs
- how to test real amounts
- what the graph says about the story
Think firstA canoe with a 50 kg limit
g is the rest of the gear. Which inequality fits the canoe?
Decide first, then press Next. Ask: is the limit itself allowed?
A line of story, a canoe can carry at most 50 kg of gear and the tent is 32 kg, over a number line from 0 to 30 kg. Then 32 + g ≤ 50 with ticks above 10 and 18 and a cross above 25, a closed dot at 18, and a thick shaded line from 18 back to 0. The last step shows $20 to spend and an $8 book.
See the whole ideathe big idea and the key word, in one place
The big idea
“At most” means ≤ and “at least” means ≥: the limit itself is allowed.
For exampleRiders must be at least 120 cm tall: h ≥ 120. A lift holds at most 10 people: p ≤ 10.
Easy to get wrongAsk whether the limit itself is allowed. If it is, use ≤ or ≥ and a closed dot.
Key words
- at most
- no more than: the limit or less, written ≤
- at least
- no less than: the limit or more, written ≥
Ready to use it?
- Write an inequality for a real limit.
- Graph its solutions and say what they mean.