91Ó°ÊÓ

In algebra, variables play a crucial role. They are symbols, often letters, used to represent unknown quantities in mathematical expressions and equations. Variables allow us to write algebraic equations that model real-world situations. In this exercise, the variable is represented by the letter \( x \). It stands in for the number we need to find. By using a variable, we can create a general solution that applies to similar problems with different numbers.
For example, rather than saying 'a number', we use \( x \) to illustrate that 'number'. This approach not only simplifies complex calculations but also makes it easier to manipulate mathematical expressions. Here, \( x \) becomes the placeholder for the unknown, making it central to solving the equation that models the situation described.

The word 'sum' in mathematics refers to the result of adding two or more numbers together. It is one of the fundamental operations in arithmetic and algebra. In our exercise, we are given that the sum of an unknown number \( x \) and 6 equals 37.
The mathematical expression for this scenario can be written as \( x + 6 \). The '+' symbol represents the addition operation here, and the whole expression indicates that when \( x \) and 6 are added together, they yield the total of 37. Understanding the term 'sum' is essential as it guides us in formulating the initial equation needed to solve the problem.

Solving an algebraic equation involves finding the value of the variable that makes the equation true. In our example, the equation is \( x + 6 = 37 \). The aim is to isolate the variable \( x \) on one side of the equation to determine its value.
To solve for \( x \), we perform the inverse operation of addition, which is subtraction. By subtracting 6 from both sides of the equation, we maintain equality and simplify the equation to \( x = 31 \).
This solution shows that replacing \( x \) with 31 satisfies the original equation, as adding 6 to 31 indeed results in 37. This step-by-step approach is fundamental in algebra for finding unknown values.