9.4 Inequalities on a number line and set notation — Practise with help
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Write and in order, smallest first.
- Which is greater, or ?
Check the warm-up
- , then .
- .
If an answer differs, revisit Section 1.1 for ordering numbers and Section 1.3 for negative numbers.
Practise with help
1. Which is greater: or ?
Hint
Use their positions on a number line.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
lies to the right, so .
2. Write “ is less than 5” in symbols.
Hint
Use a strict inequality symbol.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
.
3. Describe .
Hint
Say whether 2 is included and which direction works.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
All values at least 2; include 2 and shade right.
4. Show on a number line.
Hint
Choose an open boundary at and a filled one at 3.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
Shade between them; is excluded and 3 included.
5. List the integer values in .
Hint
Start at the included lower boundary and stop before 4.
Next step
Try the first operation or write the equation before opening the full solution.
Full working
.