4j+8=鈥8+2j

Championisme authors

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20-10-2024

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In this article, we will break down the equation 4j + 8 = 8 + 2j step by step, providing a clear understanding of how to approach similar algebraic equations. We will also delve into some practical examples and tips that can help reinforce your understanding of algebra.

Understanding the Equation

At its core, the equation is a linear equation in one variable, ( j ). Linear equations can often be solved through simple algebraic manipulations, such as isolating the variable on one side.

Step-by-Step Solution

1. Start with the original equation: [ 4j + 8 = 8 + 2j ]

2. Eliminate common terms: To simplify the equation, we can first subtract ( 2j ) from both sides: [ 4j - 2j + 8 = 8 + 2j - 2j ] This simplifies to: [ 2j + 8 = 8 ]

3. Isolate the variable: Next, we can subtract 8 from both sides: [ 2j + 8 - 8 = 8 - 8 ] This results in: [ 2j = 0 ]

4. Solve for ( j ): Finally, we can divide both sides by 2: [ j = \frac{0}{2} ] Thus, we find: [ j = 0 ]

Analysis of the Solution

The solution indicates that the value of ( j ) that satisfies the equation ( 4j + 8 = 8 + 2j ) is ( j = 0 ). This means that when you substitute ( 0 ) for ( j ) in the original equation, both sides will equal the same number (8), validating our solution.

Practical Example

To illustrate the importance of understanding how to solve linear equations, consider a real-life scenario where you need to balance a budget. If you have a monthly income represented by the expression ( 4j + 8 ) (where ( j ) stands for a variable expense), you might want to know how much you can afford to spend if you also have a fixed amount of expenses represented by ( 8 + 2j ). Finding the break-even point (where income equals expenses) allows you to make informed financial decisions.

Tips for Solving Linear Equations

1. Keep it balanced: Whatever operation you perform on one side of the equation, do the same on the other side to maintain equality.

2. Combine like terms: Always look to combine similar terms to simplify your equation before moving to isolate the variable.

3. Check your work: After solving for the variable, substitute it back into the original equation to ensure that both sides are equal. This confirms your solution is correct.

Conclusion

In summary, the equation ( 4j + 8 = 8 + 2j ) simplifies neatly to ( j = 0 ). Understanding how to manipulate and solve linear equations is a critical skill in mathematics and can apply to many real-world situations, from budgeting to programming. By practicing these types of equations, you can improve your problem-solving skills and confidence in algebra.

By breaking down the problem in this way, we not only solved the equation but also equipped ourselves with valuable strategies for tackling similar problems in the future. Understanding these concepts is vital for anyone looking to enhance their mathematical literacy.