Maths256 views·Updated Jun 14, 2026·2 pages

Understanding and Solving Inequalities

saskia wilson@saskiawilson_fuaw

Inequalities are mathematical statements that compare two values, showing which...

of 2

$Inequalaties! $a < b$ $a$ is smaller than $b$ $a > b$ $a$ is greater than $b$ $a \geq b$ $a$ is $\substack{greater \text{or} \text{$

Understanding Inequality Symbols

Think of inequality symbols as mathematical ways to say "bigger than" or "smaller than" - just like comparing your height to your mate's! The symbol $a < b$ means " $a$ is smaller than $b$ ", whilst $a > b$ means " $a$ is greater than $b$ ".

The symbols $a \geq b$ and $a \leq b$ are even more flexible. They mean "greater than or equal to" and "smaller than or equal to" respectively. This is brilliant when you need to include the boundary value itself.

Number lines make inequalities visual and easy to understand. When you see $x > 4$ , imagine all numbers to the right of 4 on a number line. For $x \leq 4$ , you'd include 4 itself (shown with a filled circle) plus everything to the left.

Quick Tip: Remember that $2 < x \leq 7 $means$ x$ is trapped between 2 and 7, where 2 isn't included but 7 is!

of 2

$Inequalaties! $a < b$ $a$ is smaller than $b$ $a > b$ $a$ is greater than $b$ $a \geq b$ $a$ is $\substack{greater \text{or} \text{$

Solving Inequalities Step by Step

Solving inequalities works almost exactly like solving regular equations - you can add, subtract, multiply, and divide both sides to isolate the variable. The process feels familiar once you get the hang of it.

For example, with $x + 4 < 8$ , you'd subtract 4 from both sides to get $x < 4$ . Simple as that! Most inequality problems follow this straightforward approach without any tricks.

Here's the crucial bit that catches everyone out: when you multiply or divide by a negative number, you must flip the inequality sign! So if you have $-2x < 6$ and divide both sides by $-2$ , the inequality becomes $x > -3$ (notice the sign flipped from < to >).

Memory Trick: Think of negative numbers as "opposite day" - everything gets reversed, including your inequality sign!

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Maths256 views·Updated Jun 14, 2026·2 pages

Understanding and Solving Inequalities

saskia wilson@saskiawilson_fuaw

Add to Google sources

Inequalities are mathematical statements that compare two values, showing which one is larger or smaller. They're everywhere in real life - from age restrictions to speed limits - and understanding them will help you solve problems involving ranges and boundaries.

of 2

$Inequalaties! $a < b$ $a$ is smaller than $b$ $a > b$ $a$ is greater than $b$ $a \geq b$ $a$ is $\substack{greater \text{or} \text{$

Understanding Inequality Symbols

Quick Tip: Remember that $2 < x \leq 7 $means$ x$ is trapped between 2 and 7, where 2 isn't included but 7 is!

of 2

$Inequalaties! $a < b$ $a$ is smaller than $b$ $a > b$ $a$ is greater than $b$ $a \geq b$ $a$ is $\substack{greater \text{or} \text{$

Solving Inequalities Step by Step

For example, with $x + 4 < 8$ , you'd subtract 4 from both sides to get $x < 4$ . Simple as that! Most inequality problems follow this straightforward approach without any tricks.

Memory Trick: Think of negative numbers as "opposite day" - everything gets reversed, including your inequality sign!