# Rearranging Formula: Step-by-Step Guide to Solve ax - b = cx + d

• Gringo123
In summary, the formula for rearranging ax - b = cx + d to make x the subject is x = (d+b)/(a-c). This is achieved by first collecting all the x terms on one side and all the non-x terms on the other side, and then factoring out x and dividing both sides by the remaining term (a-c).
Gringo123
I have been trying to rearrange this formula to make x the subject:

ax - b = cx + d

My (wrong) attempt at the answer was:

x = cx + d/a - b

I know that that is wrong because x still appears on the right side of the formula. The right answer is:

x = (d+b)/(a-c)

I have no idea how to arrive at that. Can anyone talk me through it step by step?
Thanks

sure: first collect all the x terms on one side by subtracting cx from both sides:

ax-cx-b=d

now collect all the non x terms on the opposite side by adding b to both sides.

ax-cx=b+d now factor out x so that it looks like x(a-c). Divide both sides by what now?

Divide both sides by (a-c) and you get:
x = (d+b) / (a-c)
Thanks a lot Denverdoc! It was very kind of you to help out.

no problem; btw there is a math forum here for various issues you may run into. fine that you posted here, but in future may wish to consider it.

## 1. How do I rearrange the formula ax - b = cx + d?

To rearrange this formula, you need to isolate the variable on one side of the equation and move all the constants to the other side. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.

## 2. What is the first step in solving this equation?

The first step is to combine like terms on both sides of the equation. This means adding or subtracting the same variables or constants on each side until there is only one variable term on one side and only constants on the other side.

## 3. How do I get the variable term on one side of the equation?

To get the variable term on one side of the equation, you need to use inverse operations. For example, if the variable is being multiplied by a number, you can divide both sides by that number. If the variable is being added or subtracted, you can use the opposite operation to move it to the other side.

## 4. Can I rearrange the formula in any order?

Yes, as long as you use inverse operations, you can rearrange the formula in any order. However, it is usually easier to have the variable term on the left side of the equation and the constants on the right side.

## 5. How do I know if I rearranged the formula correctly?

You can check your work by substituting the values of the variables into the original equation and seeing if it is true. For example, if the original equation was 2x - 3 = 4x + 5 and after rearranging it becomes x = 4, you can substitute x = 4 into the original equation and see if it is a true statement. If it is, then you have rearranged the formula correctly.

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