Idea 22of 23Builds onLess than or equal to
Graph the solutions
How do you draw every solution on a number line?
Today you'll discover
- where the dot goes
- open dot or closed dot
- which way to shade
Think firstx − 2 > 5
x − 2 is greater than 5. Which graph shows every solution?
Decide first, then press Next. Find the boundary, then test one number on each side.
The inequality x − 2 > 5 over a number line from 0 to 14. A tick above 10, crosses above 5 and 7. Then an open dot at 7, and a thick shaded line from the dot to the right. The last step shows 3x ≥ 12.
See the whole ideathe big idea and the key word, in one place
The big idea
Open dot: the boundary is left out. Closed dot: it counts. Shade toward the solutions.
Compare them< and > use an open dot: the boundary is not a solution. ≤ and ≥ use a closed dot: it is.
Easy to get wrongPut the dot at x's boundary, not at the number on the right: for 3x ≥ 12 the dot is at 4.
Key words
- open dot
- a hollow dot on a number line: that number is not a solution
- closed dot
- a filled dot on a number line: that number is a solution
Ready to use it?
- Graph the solutions of an inequality on a number line.