Solving Equations: A Comprehensive Guide to Finding 5x Given 3x - 2 6
Mathematics can often feel daunting, especially when it comes to solving equations. However, with a bit of practice and understanding, solving equations can become much more manageable. In this article, we will explore the process of solving an equation to find the value of 5x given that 3x - 2 6. We will break down the solution step by step and explain each operation to ensure clarity and ease of understanding.
Understanding the Basic Equation: 3x - 2 6
Let us start with the given equation: 3x - 2 6. This equation is a linear equation, where x is the variable we need to solve for. The equation implies that three times the value of x minus two equals six. To find the value of x, we need to isolate x on one side of the equation.
Step-by-Step Solution: Simplifying 3x - 2 6
Begin with the equation: 3x - 2 6. Our first step is to isolate the term containing x. We do this by adding 2 to both sides of the equation. This gives us: 3x - 2 2 6 2, simplifying to 3x 8. The next step is to solve for x. To do this, we divide both sides by 3. This results in: 3x / 3 8 / 3, simplifying further to x 8 / 3. This can also be written as x 2.6666666666666665.Using the Value of x to Find 5x
Now that we have determined that x 8 / 3, the next step is to find the value of 5x. This is a straightforward multiplication:
Write the expression for 5x: 5x. Substitute the value of x: 5 * (8 / 3). Perform the multiplication: 5 * (8 / 3) (5 * 8) / 3 40 / 3. This simplifies to approximately 13.333333333333334.Alternative Solution Path: A Different Approach to the Same Problem
Let's explore an alternative method to solve the equation 3x - 2 6 to find 5x:
Start with the equation: 3x - 2 6. Add 2 to both sides: 3x - 2 2 6 2, simplifying to 3x 8. To find the value of x, divide both sides by 3: x 8 / 3. Now multiply by 5 to find 5x: 5 * (8 / 3) 40 / 3, simplifying to approximately 13.333333333333334.Key Points to Remember
Always perform the same operation on both sides of the equation to maintain the balance. Isolate the variable you want to solve for by performing the inverse operations. Substitute the found value into the expression you need to evaluate, such as 5x.Conclusion
Solving the given equation and finding the value of 5x is a straightforward process. By following the steps outlined in this article, you can perform these calculations with ease. Understanding these methods not only helps solve linear equations but also fosters a deeper understanding of algebraic concepts. Practice regularly to master these skills and improve your mathematical problem-solving abilities.