Introduction

Inequalities are statements that compare two numbers or expressions.
They tell us whether one quantity is greater than, less than, or sometimes equal to another.

In this article, you will learn:

• What the symbols $>$ and $<$ mean
• How to read inequalities
• How to write simple inequalities
• How to compare numbers confidently

This article assumes you already know basic arithmetic (addition, subtraction, multiplication, division).

What Are Inequalities?

An inequality is a mathematical comparison between two values.

The two most common symbols are:

• Greater than: $>$
  • Example: $7 > 3$ means “7 is greater than 3.”
• Less than: $<$
  • Example: $2 < 5$ means “2 is less than 5.”

Key ideas:

• Inequalities do not always express equality—only comparison.
• They work with whole numbers, decimals, fractions, and even variables.

How to Read Inequalities

Some helpful reading patterns:

• $a > b$ → “$a$ is greater than $b$”
• $a < b$ → “$a$ is less than $b$”

Tips:

• The wide end of the symbol always points to the larger number.
• The pointed end always points to the smaller number.

Examples:

• $9 > 4$
• $1 < 3$
• $0.5 < 2$

Comparing Numbers

To decide whether $a > b$ or $a < b$, you can:

• Compare their positions on a number line
• Compare place values (tens, ones, tenths, etc.)
• Use intuition from arithmetic (e.g., adding makes numbers bigger)

Examples:

• $12 > 7$ because 12 is farther right on the number line.
• $3 < 3.5$ because 3.5 has a larger decimal part.
• $-2 < 1$ because negative numbers are always less than positive numbers.

Writing Your Own Inequalities

You can express real-world comparisons using inequalities.

Examples:

• “A cat weighing 4 kg is lighter than a dog weighing 9 kg”
  → $4 < 9$
• “A student scored higher on Test A (85) than Test B (72)”
  → $85 > 72$
• “A temperature of $-1^\circ$C is less than $3^\circ$C”
  → $-1 < 3$

Guidelines:

• Identify the two quantities.
• Decide which is larger.
• Use $>$ or $<$ accordingly.

Greater Than or Equal To (≥) and Less Than or Equal To (≤)

So far, you’ve seen inequalities that compare two values strictly using greater than (>) and less than (<). But sometimes two quantities can be equal as well as greater or less.
That’s where the symbols ≥ and ≤ come in.

What the Symbols Mean

• Greater than or equal to: \( a \ge b \)
  This means \(a\) is greater than \(b\) or \(a\) is equal to \(b\).
• Less than or equal to: \( a \le b \)
  This means \(a\) is less than \(b\) or \(a\) is equal to \(b\).

Examples

• \( 10 \ge 7 \)
  Ten is greater than seven, so the statement is true.
• \( 4 \le 4 \)
  Four is equal to four, so “less than or equal to” is also true here.
• \( -2 \le 3 \)
  Negative numbers are always less than positive numbers, so this is true.

How to Read Them

• \( a \ge b \) → “\(a\) is greater than or equal to \(b\)”
• \( a \le b \) → “\(a\) is less than or equal to \(b\)”

A helpful reminder:
The line under the symbol means equality is allowed.

Why These Symbols Matter

In many real‑world situations, you want to include the possibility of equality:

• “You must be 13 or older to enter.”
  → \( \text{age} \ge 13 \)
• “A bag can hold up to 20 kg.”
  → \( \text{weight} \le 20 \)
• “You need at least 60 points to pass.”
  → \( \text{score} \ge 60 \)

Drawing inequalities

• Inequalities can be drawn on a number line using an arrow
  • If it starts with a filled circle then it represents a $\le$ or $\ge$
  • If it starts with an unfilled circle then it represents a $\lt$ or $\gt$

Calculator

Exercises

1. Decide whether the statement $8 > 5$ is true or false.

   Solution

   True.
   $8$ is greater than $5$.
2. Fill in the blank with $>$ or $<$: $3 \; \_ \; 9$

   Solution

   $3 < 9$
   Because 3 is less than 9.
3. Compare the numbers: Is $-4$ greater than or less than $2$?

   Solution

   $-4 < 2$
   Negative numbers are always less than positive numbers.
4. Write an inequality comparing $7$ and $12$.

   Solution

   $7 < 12$
   Because 7 is smaller.
5. Determine whether $0.8 < 0.5$ is true or false.

   Solution

   False.
   $0.8$ is greater than $0.5$, so $0.8 < 0.5$ is not true.
6. Fill in the blank: $15 \; \_ \; 10$

   Solution

   $15 > 10$
   Because 15 is greater.
7. Compare the temperatures: $-3^\circ$C and $4^\circ$C.

   Solution

   $-3 < 4$
   Negative temperatures are less than positive ones.
8. Decide whether the statement $14 \le 9$ is true or false.

   Solution

   False.
   Fourteen is greater than nine, so “less than or equal to” is not true.
9. Fill in the blank with $\ge$ or $\le$: $$-2 \;\_\; 5$$

   Solution

   $ -2 \le 5 $
   Negative numbers are always less than positive numbers.
10. Compare the numbers and write a true inequality: $$3 \text{ and } 3$$

    Solution

    $ 3 \ge 3 $ or $ 3 \le 3 $
    Since the numbers are equal, both symbols with equality allowed are correct.