Linear InequalitiesIntroduction
Mathematics is the art of saying many things in many different ways. – MAXWELL
The Dussehra mela is in town, and the queue for the giant wheel is long. At the gate stands a painted board: Riders must be at least 120 cm tall. The man at the gate measures every child before letting them through.
Tonight, you are the man at the gate.
Drag each child into the right group.
Look at what the board did not say. It did not say "Riders must be exactly 120 cm tall" — then only Riya would ride. It allowed a whole range of heights: 120 cm, and every height above it. If is a child's height in centimetres, the rule on the board is . That is not an equation with one answer. It is an inequality, and it has a whole set of answers.
Say It With a Symbol
In earlier classes you solved equations in one and two variables, and turned word problems into equations. But many real rules do not fix a quantity — they put a limit on it. Four symbols do that job:
| Symbol | Read as |
|---|---|
| is less than | |
| is greater than | |
| is less than or equal to (is at most) | |
| is greater than or equal to (is at least) |
Translate each rule into symbols.
Every student in your class is shorter than 160 cm:
Your classroom can hold at most 60 tables and chairs in all:
You must score at least 33 marks to pass:
The halwai delivers free if the order is worth more than ₹500:
Statements like these, built with , , or , are called