Math problem - solving for a variable

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In summary, the conversation is about solving an equation with square roots on both sides. The original attempt at a solution involved squaring both sides, but with some mistakes in the calculation. The expert explains the correct steps, including using the FOIL method and substituting back in for variables, to solve the equation and obtain the correct answer of x=5/2. The person seeking help is grateful for the assistance.
  • #1
Matt1234
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Homework Statement



sqrt(2x+4) = sqrt(6x+1) - 1

I Need to solve for x, but cannot seem to get the same answer as the text. (Ans. x= 5/2)

The Attempt at a Solution



sqrt(2x+4) - sqrt(6x+1) = -1
square both sides
(2x+4) - (6x+1) = 1
-4x-3=1
-4x=4
x=-1 ??

I know I must be doing something wrong, it has been a while since I have done this sort of problem.

Thank you for your time.
 
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  • #2
Your mistake is in thinking (a-b)2 = a2-b2, which is what you did when you squared the lefthand side of the equation. You need to multiply it out correctly.
 
  • #3
Im still not there yet:

My new attempt:

[PLAIN]http://img829.imageshack.us/img829/3997/59971783.png [Broken]

I can't seem to get rid of the sqrt (x)
i know sqrt(12x) = 2*sqrt(3x)
 
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  • #4
Now you're making even more mistakes. First,

[sqrt(2x+4)-sqrt(6x+1)]2 ≠ (2x+4) - (6x+1)

Second,

sqrt(a+b) ≠ sqrt(a)+sqrt(b)

which is what you're doing going from the fifth line to the sixth line. You were, however, correct when you said earlier that

(sqrt(2x+4))2 = 2x+4
The problem is actually a bit easier to solve if you square both sides right away:

(sqrt(2x+4))2 = (sqrt(6x+1)-1)2

To correctly calculate the righthand side, let a=sqrt(6x+1) and b=1. Then your equation becomes

(sqrt(2x+4))2 = (a-b)2

Now FOIL out the righthand side and then substitute back in for a and b.
 
Last edited:
  • #5
Im sorry, I am unable to see that. All i can see is black and faint white portions. Is it possible for you to take a screen shot and upload to image shack?
 
  • #6
I edited my previous post and took out the images. You should be able to read it now.
 
  • #7
I got it, thank you for your help.
It took a while to come back to me. I appreciate your time, thank you.

[PLAIN]http://img443.imageshack.us/img443/7086/46883092.png [Broken]
 
Last edited by a moderator:
  • #8
Looks fine.
 

1. How do I solve for a variable in a math problem?

To solve for a variable in a math problem, you need to isolate the variable on one side of the equation by using inverse operations. This means that you need to perform the opposite operation of what is being done to the variable in the equation. For example, if the variable is being added, you would subtract; if the variable is being multiplied, you would divide.

2. What are the steps for solving a math problem for a variable?

The steps for solving a math problem for a variable are as follows:

  1. Identify the variable in the equation.
  2. Use inverse operations to isolate the variable on one side of the equation.
  3. Simplify both sides of the equation if necessary.
  4. Check your solution by plugging it back into the original equation.

3. Can I use the same steps to solve any math problem for a variable?

Yes, the same general steps can be used to solve any math problem for a variable. However, the specific operations and techniques used may vary depending on the type of equation and the variable being solved for.

4. What should I do if I cannot isolate the variable on one side of the equation?

If you cannot isolate the variable on one side of the equation, you may need to use a different method such as substitution or elimination. You can also try simplifying the equation further or rearranging the terms to make it easier to isolate the variable. If you are still having trouble, it may be helpful to seek assistance from a tutor or teacher.

5. How do I know if my solution to a math problem is correct?

To check if your solution is correct, you can plug it back into the original equation and see if it satisfies the equation. If the solution makes the equation true, then it is correct. You can also use a calculator or check your work step-by-step to ensure that you have not made any errors.

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