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Algebra is a branch of mathematics that uses symbols, usually letters, to represent numbers and express mathematical relationships. These symbols are known as variables. In solving basic algebra problems, we often start with a word problem that needs to be translated into an equation.
Consider the given exercise: 'The difference of a number and eight is 4. Find the number.' This tells us to find an unknown number.

We start by representing the unknown number with a variable, commonly denoted as 饾懃. Understanding the operations mentioned in the problem is crucial. For example, 'the difference of a number and eight' translates to subtracting eight from our variable 饾懃.
So, the algebraic expression for the problem is 饾懃 - 8.

Translate word problems

• Identify keywords, like 'difference' (indicating subtraction), or 'product' (indicating multiplication).
• Represent the unknown number with a variable.
• Form an equation based on the relationships described in the problem.

Equation solving involves finding the value of a variable that makes the equation true. We use algebra to manipulate the equation and isolate the variable.
In the given exercise, our equation is 饾懃 - 8 = 4. The goal is to find the value of 饾懃.

Steps to solve the equation:

• First, understand the equation: We need to get 饾懃 by itself on one side of the equation.
• To isolate 饾懃, perform the opposite operation of what is currently being done to it. Here, 8 is being subtracted from 饾懃.
• The opposite operation of subtraction is addition, so we add 8 to both sides of the equation to balance it: 饾懃 - 8 + 8 = 4 + 8.
• This simplifies to 饾懃 = 4 + 8, and further simplifies to 饾懃 = 12.

Thus, the solution to the equation is 饾懃 = 12.

Variable isolation means rearranging an equation so that the variable is on one side and everything else is on the other side. This helps us determine the value of the variable easily.
Let's revisit the given exercise. Our equation after translating the word problem is 饾懃 - 8 = 4.

To isolate 饾懃, follow these steps:

• Recognize that 饾懃 - 8 means we have 8 less than the variable 饾懃.
• Add 8 to both sides to cancel out the -8: 饾懃 - 8 + 8 = 4 + 8.
• We add 8 because adding the same number to both sides of an equation keeps it balanced.
• After performing the calculation, we get: 饾懃 = 12.

This process leaves the variable isolated and the equation balanced, giving the solution.

Always verify your solution

• Substitute the value back into the original equation.
• Check if it satisfies the condition of the problem.

For our solution, substituting 饾懃 = 12 back gives 12 - 8 = 4, which confirms it's correct.