Solving Equations: A Step-by-Step Guide with 4x-1248
Mathematics, particularly algebra, forms the cornerstone of many complex problem-solving tasks. Understanding how to solve linear equations is essential for students and professionals alike. In this guide, we will walk through the process of solving the equation 4x - 12 48, providing a clear and detailed explanation of each step along the way.
Understanding the Equation
An equation is a statement that asserts the equality of two expressions. In the context of algebra, we often deal with linear equations, which involve variables and constants, and are typically of the form ax b c. Our target equation is 4x - 12 48.
Step-by-Step Solution
Let's solve this equation step by step to understand how to find the value of x.
Step 1: Isolate the Variable Term
First, we need to isolate the term containing the variable x. To achieve this, we add 12 to both sides of the equation:
4x - 12 48
4x - 12 12 48 12
By performing the addition, we simplify the equation:
4x 60
Step 2: Isolate the Variable
Now that we have isolated the term with x, the next step is to isolate x by dividing both sides by 4:
4x 60
4x ÷ 4 60 ÷ 4
This simplifies to:
x 15
Verification and Proof
To confirm that our solution is correct, we can substitute x 15 back into the original equation 4x - 12 48:
4(15) - 12 48
60 - 12 48
48 48
The left side equals the right side, thus proving that x 15 is indeed the solution to the equation.
Conclusion
Mastery of algebraic problem solving, such as solving the equation 4x - 12 48, is crucial for students and professionals in various fields, including science, engineering, and finance. Understanding the step-by-step process will not only help in finding the solution but also in verifying and applying it in real-world scenarios.