Idea 21of 23Builds onAn inequality has many solutions
Less than or equal to
What does the line under ≤ and ≥ add?
Today you'll discover
- what the line under the sign adds
- why the boundary now counts
- how to find the smallest solution
Think firstx + 4 ≤ 10
Does x = 6 make x + 4 ≤ 10 true?
Decide first, then press Next. Ask: is equal allowed?
The inequality x + 4 ≤ 10 over a number line from 0 to 12, with the line: ≤ means less than or equal to, at most. Ticks above 3 and 6, a cross above 8. Then a closed dot at 6. The last step shows x − 3 ≥ 9.
See the whole ideathe big idea and the key word, in one place
The big idea
≤ and ≥ include the boundary: the two sides may also be equal.
Four signs
Read each sign from the left side to the right.
- <less than
- >greater than
- ≤at most
- ≥at least
Easy to get wrongx + 4 ≤ 10 and x + 4 < 10 differ by one number: 6 works for ≤ but not for <.
Key word
- or equal to
- the line under ≤ and ≥: the two sides may also be equal
Ready to use it?
- Decide whether the boundary is a solution.
- Find the smallest or largest solution.