What is a Linear Inequality?
You are already familiar with equations like , which say that something equals a specific value. But in real life, things are often within a range rather than exactly one value. That's where inequalities come in.
A mathematical statement that compares two expressions using symbols like , , , or , showing that one quantity is greater than, less than, or equal to another.
An inequality involving a variable raised only to the power of 1 (no squared terms, no fractions with variables). For example: or .
The four inequality symbols are:
| Symbol | Meaning | Example |
|---|---|---|
| less than | ||
| greater than | ||
| less than or equal to | ||
| greater than or equal to |
Think of the inequality symbol as a hungry crocodile — it always opens its mouth toward the bigger number. So means the crocodile eats the 3 because 3 is bigger.
The Number Line: A Quick Recap
Before we represent inequalities, let's make sure the number line is clear in your mind.
A number line extends infinitely in both directions from zero:
- Numbers to the right of zero are positive integers:
- Numbers to the left of zero are negative integers:
- Zero is neither positive nor negative.
Two key rules to remember:
- As you move left to right, numbers increase.
- As you move right to left, numbers decrease.
Ordering numbers on the number line:
Which is greater, or ?
is further to the right on the number line, so .
Which is smaller, or ?
is further to the left, so .
Pairs like and are called opposites — they are the same distance from zero but on opposite sides.
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