Solving Simple Algebraic Equations: A Step-by-Step Guide

Algebra can be a powerful tool for solving a wide range of problems. However, sometimes the problems might seem trivial, but still require a systematic approach to find the solution. Let's take a look at a simple equation that requires a bit of algebraic thinking:

If a number is multiplied by two and four is added to it the result is ten. What is the number?

Understanding the Problem

This problem can be represented algebraically as:

2x 4 10

Solving the Equation Step-by-Step

Let's start by subtracting 4 from both sides to isolate the term with the variable x: 2x 4 - 4 10 - 4 2x 6 Next, we divide both sides by 2 to solve for x: 2x / 2 6 / 2 x 3

Alternative Methods

Some might solve this problem without using algebra, instead working backward from the known result. Here are a few alternative methods:

Method 1:

Start with the result: 10 Subtract 4: 10 - 4 6 Divide by 2: 6 / 2 3

Method 2:

Assume the number is x Set up the equation: 2x 4 10 Subtract 4 from both sides: 2x 6 Simplify: x 3

Key Points to Remember

Algebra can be simplified: Not all algebraic problems need complex solutions. Some can be solved with simple arithmetic operations. Reversing operations: Always consider reversing the order of operations to simplify the problem. Prioritize clarity: Writing out each step can help ensure accuracy and provide a clear path to the solution.

Conclusion

While this problem seems straightforward, understanding the underlying algebraic principles can help you approach similar problems with confidence. By breaking down the steps and using simple arithmetic, even complex algebraic equations can be solved easily. Remember, the key is in comprehending the problem and then systematically solving it.