# Rearrange Equations: Making J the Subject - Need Help

• peter_pan
In summary, the process for making J the subject of an equation involves isolating J on one side and rearranging the terms on the other side using inverse operations. Any equation with J as a variable can be rearranged, but common mistakes to avoid include not applying operations to both sides and not properly isolating the variable. Tips for solving equations more efficiently include identifying which terms to move and using inverse operations. To check the correctness of a rearranged equation, you can substitute J back into the original equation or graph both equations.
peter_pan
SO here is the problem

I am wondering how to make J the subject ?

I have tried making J/2 and 4a/3 into a single fraction but so far nothing.I am doing something wrong somewhere.

Any suggestions ?

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Here it is so I can see it better:
$$V = \frac{\frac{J}{2} + \frac{4a}{3}}{L}$$

Multiply both sides by L.
Subtract 4a/3 from both sides.
Multiply both sides by 2.

Sure, I can help with rearranging equations to make J the subject. First, let's clarify what we mean by "making J the subject." This simply means isolating J on one side of the equation, with all other variables and numbers on the other side. To do this, we can use algebraic operations such as addition, subtraction, multiplication, and division.

Let's take a look at the equations you provided. You mentioned trying to make J/2 and 4a/3 into a single fraction, but you were unsuccessful. It's important to remember that when combining fractions, we need to have a common denominator. So, for J/2 and 4a/3, we can rewrite them as (3J/6) and (8a/6), which have a common denominator of 6. Now, we can combine them into a single fraction: (3J+8a)/6.

Next, we need to isolate J on one side of the equation. We can do this by subtracting 8a from both sides, giving us (3J+8a)/6 - 8a = 0. Simplifying this, we get (3J - 40a)/6 = 0. Now, we can multiply both sides by 6 to get rid of the fraction, giving us 3J - 40a = 0. Finally, we can add 40a to both sides to isolate J, giving us the final equation: J = 40a/3.

So, in summary, to make J the subject, we combined the fractions, isolated J on one side of the equation, and solved for J. I hope this helps! Let me know if you have any other questions or if you need further clarification.

## 1. What is the process for making J the subject of an equation?

The process for making J the subject of an equation involves isolating J on one side of the equation and rearranging the terms on the other side to solve for J. This typically involves using inverse operations, such as addition and subtraction, multiplication and division, and exponentiation, to move the terms around.

## 2. Can any equation be rearranged to make J the subject?

Yes, any equation that contains J as a variable can be rearranged to make J the subject. However, the complexity of the rearranging process may vary depending on the equation and the operations involved.

## 3. What are some common mistakes to avoid when rearranging equations to make J the subject?

Common mistakes to avoid include not applying the same operation to both sides of the equation, forgetting to use the distributive property, and not properly isolating the variable on one side of the equation.

## 4. Are there any tips for solving equations to make J the subject more efficiently?

One tip is to start by identifying which terms need to be moved to the other side of the equation in order to isolate J. Another tip is to use the inverse operation of each term to move it to the other side. It can also be helpful to work with one variable at a time and simplify the equation as much as possible before rearranging.

## 5. How can I check if my rearranged equation to make J the subject is correct?

You can check your rearranged equation by substituting the value of J back into the original equation and seeing if both sides are equal. Another method is to graph both the original and rearranged equations and see if they produce the same graph.

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