# Need help making sure I'm doing a substitution correctly

• EGill
In summary, the conversation comprised of discussing a word document that contained work and equations. The first equation was correctly manipulated, but the second equation had an error. The person seeking help was advised to multiply the x term and separate the variables. Eventually, the correct equation was obtained, but there was still a point of confusion about using the same constant in different places. Finally, there was discussion about how to input LaTeX code in the reply and the need to refresh the page to view changes in the equation area.
EGill
I have attached a word document that shows all the work and equations.

#### Attachments

• problem 3.10.doc
95 KB · Views: 213
$$x\left[\frac{dv(x)}{dx}+1\right]=\left[v(x)\right]^{3}+v(x)+x$$

$$\mbox{ is correct, but the equation after it}$$

$$f \left[\frac{1}{v(x)^{3}}+\frac{1}{v(x)}\right]dv=\frac{1}{x}dx$$

$$\mbox{does not follow- you incorrectly manipulated the first equation.}$$

$$\mbox{Try multiplying the x through in the } x\left[\frac{dv(x)}{dx}+1\right]\mbox{ term, and then try to separate the variables.}$$

Thanks for the response. Took forever, but I have managed to do it correctly further along now.

I am still stuck at another point. The new attachment shows all my work again

#### Attachments

• problem 3.10.doc
162 KB · Views: 205
You have an error.
I'm assuming that your work is correct up to where you said you're confident.

ln(u - x) - (1/2)ln[(u - x)2 + 1] = ln(x) + C

<==> ln(u - x) - ln[(u - x)2 + 1]1/2 = ln(x) + C

Now combine the two log terms on the left side using the property that ln(a) - ln(b) = ln(a/b).

Also, on the right side you have eln(x) + C becoming Cx. The first C is different from the second C. They're both constants, but they are different ones, so you should use a different letter or mark the second one to note that they are different.

$$ln\left[\frac{u-x}{((u-x)^2+1)^{1/2}}\right]=e^{ln\left[x\right]+c$$

$$\frac{u-x}{((u-x)^2+1)^{1/2}}=Dx$$

Would this be correct? Since C is a dummy variable i figured I could reuse it, but I see your point.

Also, this was my first time trying to type a formula into the reply. Whenever I hit preview post it would refresh, but the post would not reflect the changes in the equation area. I had to reload the page to get the post to reflect the changes in equation. Am I doing something wrong. Just trying to learn how to do it without word docs if it is just one equation.

Last edited:
That is correct. And no, you aren't doing something wrong inputting Latex code.. for some reason you have to refresh the page to view changes using preview post.

EGill said:
Also, this was my first time trying to type a formula into the reply. Whenever I hit preview post it would refresh, but the post would not reflect the changes in the equation area. I had to reload the page to get the post to reflect the changes in equation. Am I doing something wrong. Just trying to learn how to do it without word docs if it is just one equation.
As I understand things, the LaTeX script is cached on your computer, so when you start a post and click Preview Post, the previous LaTeX script, if any, is displayed, not the script you just entered. This is a known problem. The workaround is to refresh the web page. That will display the right LaTeX script.

## 1. How do I know if I am using the correct substitution method?

The best way to ensure you are using the correct substitution method is to carefully read through your problem and identify the variable you need to isolate. Then, choose the substitution method that will allow you to eliminate that variable and solve for the remaining one.

## 2. What are some common mistakes to avoid when using substitution?

One common mistake is forgetting to substitute the entire expression for the variable, including any coefficients. Another mistake is not distributing a negative sign when necessary. It is also important to double check your work after substituting to make sure the resulting equation is correct.

## 3. When should I use substitution instead of other algebraic methods?

Substitution is best used when one of the equations contains a variable with a coefficient of 1 or -1. It is also useful when one of the equations is already solved for a variable, making it easier to substitute into the other equation.

## 4. What should I do if I am having trouble solving a problem with substitution?

If you are having trouble solving a problem with substitution, try working through the problem step by step and checking your work after each step. It may also be helpful to review the steps and examples of substitution in your textbook or seek additional help from a teacher or tutor.

## 5. Can I use substitution to solve any type of algebraic equation?

No, substitution can only be used to solve systems of equations where one equation can be solved for a variable. It cannot be used to solve equations with more than two variables or equations with no solution.

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