🗺️ Chapter Roadmap
1 What is an Inequality?
In an Equation, two things are exactly equal (=). In an Inequality, we compare two things that are not equal. It tells us if something is greater, smaller, or potentially equal to something else.
2 The Symbols
Example: 5 > 3
Example: 2 < 4
Example: x ≥ 10
Example: x ≤ 10
3 Solving Step-by-Step
For addition and subtraction, an inequality behaves exactly like an equal sign (=). You move numbers across and change their signs (+ becomes −).
📝 Simple Example:
Move +5 to other side → x > 12 − 5
x > 7
(This means any number larger than 7, like 8, 9, 10... is a solution)
4 ⚡ The Golden "Negative" Rule
This is the only difference between equations and inequalities, and it is a favorite for examiners to use as a trap.
⚠️ Alert Rule
"When you multiply or divide an inequality by a NEGATIVE number, you must FLIP (reverse) the direction of the sign."
The Trap
−2x > 10
Divide both sides by −2...
x < −5
(Notice how > flipped to <)
Why? Think of numbers.
10 is greater than 5.
But −10 is less than −5.
Multiplying by a negative flips the world!
5 Number Line Representation
When drawing an inequality on a number line, pay attention to the circle:
The number itself is not included. (Start from here but don't touch it).
The number itself is included. (It is part of the solution).