- Ordering Rounding and Order of Operations
- Home
- Introduction to Inequalities
- Comparing a Numerical Expression With a Number
- Ordering Large Numbers
- Rounding to Tens or Hundreds
- Rounding to Hundreds or Thousands
- Rounding to Thousands, Ten Thousand, or Hundred Thousand
- Estimating a Sum of Whole Numbers
- Estimating a Difference of Whole Numbers
- Estimating a Product of Whole Numbers
- Estimating a Quotient of Whole Numbers
- Writing Expressions Using Exponents
- Introduction to Exponents
- Power of 10: Positive Exponent
- Power of 10: Negative Exponent
- Introduction to Parentheses
- Comparing Numerical Expressions With Parentheses
- Introduction to Order of Operations
- Order of Operations With Whole Numbers
- Order of Operations With Whole Numbers and Grouping Symbols
- Order of Operations With Whole Numbers and Exponents: Basic

# Introduction to Inequalities

An **inequality** is a mathematical statement which shows that two values are not equal.

** a ≠ b** means that

*a*is not equal to

*b*. It means that either

*a*is less or greater than

*b*.

There are **special symbols** that show how things are not equal.

** a < b** means that

*a*is less than

*b*

**a > b** means that

*a*is greater than

*b*

** a ≤ b** means that

*a*is less than or equal to

*b*

** a ≥ b** means that

*a*is greater than or equal to

*b*

To compare two numbers, we use the symbols, <, > or =.

**Example**

Use <, >, or = to compare the numbers given below

18 | 21 |

72 | 38 |

109 | 163 |

**Solution**

**Step 1:**

Since 18 is less than 21 we write 18 󠄀< 21

**Step 2:**

As 72 is greater than 38, we write 72 > 38

**Step 3:**

As 109 is less than 163, we write 109 < 163

Use <, >, or = to compare the numbers given below

15 | 23 |

67 | 41 |

127 | 199 |

336 | 153 |

### Solution

**Step 1:**

Since 15 is less than 23 we write 15 󠄀< 23

**Step 2:**

As 67 is greater than 41, we write 67 > 41

**Step 3:**

As 127 is less than 199, we write 127 < 199

**Step 4:**

As 336 is greater than 153, we write 336 > 153

Use <, >, or = to compare the numbers given below

29 | 18 |

78 | 97 |

172 | 146 |

331 | 463 |

### Solution

**Step 1:**

Since 29 is greater than 18, we write 29 󠄀> 18

**Step 2:**

As 78 is less than 97, we write 78 < 97

**Step 3:**

As 172 is greater than 146, we write 172 > 146

**Step 4:**

As 331 is less than 463, we write 331 > 463