## Greater than or equal to

The greater than or equal to sign is a mathematical symbol that denotes an inequality between two values or numbers. It is a form in which strokes of two equal lengths connect at an acute angle at the right. These signs are classified as:

- The greater than symbol is (>). For example, if 6>3, we will read it as “6 is greater than 3′.
- The less than symbol (<). For example, if 6<3, we will read it as “6 is less than 3′.
- greater than or equal (≥). For example, if 6≥3, we will read it as “6 is greater than or equal to 3′.
- less than or equal to (≤). For example, if 6≤3, we will read it as “6 is less than or equal to 3′.

All these symbols reduce time complexity and make understanding easier. A typical use of greater than symbol is to compare two values. The first number is greater than the second number, or one value is greater than the other. The application of this symbol is in descending order, where the arrangement from the largest to smallest number is done using it. This is an approximation of a closing angle bracket.

**Symbols with Examples**

Do we know what greater than or equal to sign means? The following table shows the symbols with its definition and examples in detail.

Symbol | Description | Example |

= | Equal to | 3+4 = 7 |

≠ | Not equal to | 4 + 3 ≠ 5 |

> | Greater than | 6 > 3 |

≥ | Greater than or equal to | Students ≥ 6 |

< | Less than | 3 < 9 |

≤ | Less than or equal to | Students ≤ 60 |

**How to use these symbols?**

The symbols might be very confusing when it comes to their application. There are some methods to understand it better. These methods are as follows:

- Understanding symbols using points
- Alligator method
- L method

We will now discuss these methods in brief.

**1. Understanding symbols using points**

- Greater than symbol (>)

Understand the symbol from the left side to the right side. On the left hand, it has two points, and on the right side, it has one point. So write the symbol (>).

- Less than symbol (<)

Understand the symbol from the left side to the right side. On the left hand, it has one point, and on the right side, it has two points. So write the symbol (<).

**2. Alligator Method**

- The crocodile or the alligator method is easy to understand, and it’s a famous method.
- Let us assume the (<) crocodile and the numbers on both sides to be its food.
- The crocodile is always hungry and wants to eat a lot of food, so its mouth will open where the food is in more significant numbers.
- We assume that the values on both sides represent the number of fish. For example, 9>2 Here, the alligator’s mouth opens towards the value nine, which means that nine is greater than 2.

**3. L method**

- The letter ‘L’ resembles the less than symbol “< “
- The trick to remembering how the less than sign looks is very simple. As “less than” starts with l, the symbol < looks more like the letter L.

#### Some Examples to understand more about the symbols:

- 4>2, which denotes that 4 is greater than 2.
- 2<6, which denotes that 2 is less than 6.
- 2
^{4}>2, which denotes 2×2×2×2 = 16 is greater than 2. - (10/2)>(4/2), which denotes 5>2.
- -1<-2, -1 is less than -2.
- 0.1>0.00001, here the value 0.1 is greater than 0.00001

**Greater Than or Equal To symbol**

The greater than or equal symbol represents inequality in math. It tells that the given value is greater than or equal to a particular value. This symbol is for linear inequalities where we don’t know if the variable’s value is greater than or equal to a specific value. This symbol is the “greater than” symbol ( >) with a line under it. The line below the greater sign means “equal to”. For example, x ≥ 6 means that x is either greater than or equal to 6. It defines a range of values that x can take, which starts from 6 and goes to infinity.

- The word “greater than” expresses that one quantity is greater than the other quantity.
- The “is equal to” expresses that two quantities are equal.
- When these terms are combined, they make a new term, Greater Than Or Equal To.
- This term shows, that the quantity or amount value limit could be equal to or greater than the limit given.

**Some examples of greater than or equal to:**

Q.Express x ≥ 17 equation in word form.

A.Here, x is greater than or equal to 17.

Q.Raj needs to score greater than or equal to 50% marks to clear the exam. Express this by using inequality.

A.x ≥ 50%

**How to Solve Word Problems of Inequality**

Start solving the problem by:

- Reading it thoroughly
- Highlight the details
- Recognize the variables
- Write down the equation on paper
- Solve the given problem statement
- Write the solution with complete sentences

**Solved Examples:**

**Example 1: **Dev has ₹500 rupees in his account at the beginning of the summer. He withdraws ₹25 every week and wishes to have at least ₹200 in the bank account by the end of the summer—Express Dev’s situation using the inequality symbol.

**Solution: **Let x be the number of weeks

Therefore, the inequality expression is

500 – 25x ≥ 200

Here the symbol (≥) fits as Dev wants to have money equal to greater than 200 by the end of the summer.

**Example 2: **A fruit shop owner sells a glass of juice for ₹50. He targets to earn money greater than or equal to ₹5000 in a day. Write an inequality representing this situation.

**Solution:** Cost of each glass of juice = ₹50

Let x equal the number of glasses of juice he sells in a day

Therefore, the total cost of x glasses of juices he sells in a day = ₹50x

The total earnings should be greater than or equal to ₹5000 a day.

So the inequality to represent this is 50x ≥ 5000.

**Example 3: **Minimum marks that John needs to score are 50 out of 100 to clear his math exam. Represent this statement using the greater than or equal to inequality symbol.

**Solution:** Let x be marks of John.

We know that the passing marks are 50 or more.

The inequality, x ≥ 50, represents the above situation.

Here x is the number of marks scored by John.

**Example 4: **Find the numbers that belong to the following set {x ∈ N / x ≥ 6 }.

**Solution:** Here, N is the set of natural numbers.

The given set is: {x ∈ N / x ≥ 6 }

It means that we have to find all the natural numbers greater than or equal to 6.

As the set of natural numbers is up to infinite, numbers that belong to the given set are 6,7,8,9,……to infinity.

**Example 5: **Sourav scored 30 marks in his maths exam. Riya scored 24 in the same exam. Who scored less?

**Solution: **Given data:

Marks scored by Sourav= 30 marks,

Marks scored by Riya= 24 marks

The inequality will be 24<30. Therefore, Riya scored less than Sourav.

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