Discover Mathematics P6: Term 1, Unit 4, Lessons 1–3
GoalRead and write inequalities from real limits and show them on a number line.
New words
inequality · a statement that uses <, >, ≤ or ≥ instead of =at most / at least · at most means ≤, at least means ≥solution set · all the values that make the inequality true
Explanation
Many signs give a limit, not one exact value: a speed limit of 90 km/h, a ride for children at least 120 cm tall, a price under 50 LE. An inequality uses these symbols: < less than, > greater than, ≤ less than or equal to, ≥ greater than or equal to. “At most 40” means ≤ 40 and “at least 120” means ≥ 120. An inequality usually has many solutions. On a number line we draw an open circle if the end value is not included (< or >), a filled circle if it is included (≤ or ≥), and an arrow towards the values that work.
In words
Symbol
more than
>
fewer than / less than
<
at least
≥
at most
≤
Worked examples
A road sign says the speed limit is 90 km/h. A car’s speed s must be at most 90, so s ≤ 90. The circle at 90 is filled because exactly 90 km/h is allowed. The arrow points left to all slower speeds.
x > 4 means x is more than 4. The circle at 4 is open because 4 is not a solution. 5, 6, 4.5 and 100 are solutions.
A ride sign says children must be at least 120 cm tall. The height h satisfies h ≥ 120. The circle at 120 is filled: a child who is exactly 120 cm may ride, but 119 cm may not.
Class activity
Sign hunt. On a walk, look for signs or notices that give a limit: a speed limit, a maximum weight, an age or height rule, a price cap. Write each as an inequality with a letter and say whether the end value is included. Draw one of them on a number line.
Practice
1
A hall can hold at most 40 pupils. Write an inequality for the number of pupils n.
n ≤ 40.
2
A basket has fewer than 12 apples. Write an inequality for the apples a.
a < 12.
3
Is 4 a solution of x > 4? Is it a solution of x ≥ 4?
No for x > 4, because 4 is not more than 4. Yes for x ≥ 4.
4
Which inequality does the graph show?
x < 3. The open circle at 3 means 3 is not included, and the arrow points to smaller numbers.
5
A lift allows at most 8 people. Can exactly 8 ride? Can 9?
