Equal Sign

The equal sign (=) is a mathematical symbol that indicates equality between two expressions or values. It is one of the most fundamental symbols in mathematics and is used in a wide variety of contexts.

History of the Equal Sign

The equal sign was first used in the 16th century by the Welsh mathematician Robert Recorde. Recorde used the symbol to represent the Latin phrase “aequalis est,” which means “is equal to.” The symbol quickly gained popularity and was soon adopted by other mathematicians.

Usage of the Equal Sign

The equal sign is used in a variety of mathematical contexts, including:

• Equations: An equation is a mathematical statement that asserts that two expressions are equal. For example, the equation 3x + 5 = 10 states that the expression 3x + 5 is equal to the expression 10.
• Inequalities: An inequality is a mathematical statement that asserts that two expressions are not equal. For example, the inequality 3x + 5 > 10 states that the expression 3x + 5 is greater than the expression 10.
• Assignments: An assignment is a mathematical statement that assigns a value to a variable. For example, the assignment x = 5 assigns the value 5 to the variable x.

Properties of the Equal Sign

The equal sign has a number of important properties, including:

• Reflexivity: The equal sign is reflexive, meaning that any expression is equal to itself. For example, 3 = 3.
• Symmetry: The equal sign is symmetric, meaning that if two expressions are equal, then the order of the expressions can be reversed without changing the truth of the statement. For example, if 3 = 5, then 5 = 3.
• Transitivity: The equal sign is transitive, meaning that if two expressions are equal to a third expression, then the two expressions are equal to each other. For example, if 3 = 5 and 5 = 7, then 3 = 7.

Not Equal Sign

The not equal sign is a mathematical symbol that is used to indicate that two expressions are not equal to each other. It is represented by the symbol ≠.

How to Use the Not Equal Sign

The not equal sign is used in mathematical expressions to compare two values. If the two values are not equal, then the expression will evaluate to true. Otherwise, the expression will evaluate to false.

For example, the expression 5 ≠ 3 evaluates to true because 5 is not equal to 3. The expression 5 ≠ 5 evaluates to false because 5 is equal to 5.

Examples of the Not Equal Sign

The not equal sign can be used in a variety of mathematical expressions. Here are a few examples:

• 5 ≠ 3
• x ≠ y
• a + b ≠ c
• sin(x) ≠ cos(x)

Conclusion

The not equal sign is a useful mathematical symbol that can be used to compare two values. It is important to understand how to use the not equal sign in order to write correct mathematical expressions.

Use of Equal Sign

The equal sign (=) is one of the most commonly used symbols in mathematics and programming. It is used to indicate that two expressions have the same value. For example, in the equation 3 + 4 = 7, the equal sign indicates that the sum of 3 and 4 is equal to 7.

In Mathematics

In mathematics, the equal sign is used to denote equality between two expressions. For example, in the equation 3 + 4 = 7, the equal sign indicates that the sum of 3 and 4 is equal to 7.

The equal sign can also be used to define variables. For example, in the equation x = 5, the equal sign indicates that the variable x is assigned the value 5.

In Other Fields

The equal sign is also used in other fields, such as physics, chemistry, and engineering. In physics, the equal sign is used to denote equality between two forces. In chemistry, the equal sign is used to denote equality between two chemical reactions. In engineering, the equal sign is used to denote equality between two measurements.

The equal sign is a versatile symbol that is used in a variety of fields. It is used to indicate equality between two expressions, to define variables, and to compare two values.

Equal Sign Solved Examples

Example 1: Solving a Simple Equation

Let’s solve the equation 3x + 5 = 17 for x.

Step 1: Subtract 5 from both sides

3x + 5 - 5 = 17 - 5 3x = 12

Step 2: Divide both sides by 3

3x/3 = 12/3 x = 4

Therefore, the solution to the equation 3x + 5 = 17 is x = 4.

Example 2: Solving an Equation with Variables on Both Sides

Let’s solve the equation 2x + 3 = 5x - 7 for x.

Step 1: Move all the terms with x to one side

2x - 5x = -7 - 3 -3x = -10

Step 2: Divide both sides by -3

-3x/-3 = -10/-3 x = 10/3

Therefore, the solution to the equation 2x + 3 = 5x - 7 is x = 10/3.

Example 3: Solving an Equation with Fractions

Let’s solve the equation 2/3x + 1/4 = 5/6 for x.

Step 1: Multiply both sides by the least common multiple of the denominators, which is 12

12 * 2/3x + 12 * 1/4 = 12 * 5/6 8x + 3 = 10

Step 2: Subtract 3 from both sides

8x + 3 - 3 = 10 - 3 8x = 7

Step 3: Divide both sides by 8

8x/8 = 7/8 x = 7/8

Therefore, the solution to the equation 2/3x + 1/4 = 5/6 is x = 7/8.

Example 4: Solving an Equation with Decimals

Let’s solve the equation 0.5x + 1.2 = 3.7 for x.

Step 1: Subtract 1.2 from both sides

0.5x + 1.2 - 1.2 = 3.7 - 1.2 0.5x = 2.5

Step 2: Divide both sides by 0.5

0.5x/0.5 = 2.5/0.5 x = 5

Therefore, the solution to the equation 0.5x + 1.2 = 3.7 is x = 5.