Solve for 'x' (with 4 variables and 1 equation)

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In summary, the conversation discusses a problem involving factoring and solving for a variable in an equation. The problem is eventually corrected to be ac + bc = (a - c)(a + b) - xabcd^2 and various factoring techniques are explored, but the solution is not found. The conversation then introduces a new problem of solving for x in the equation a = b - cx.
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PhizKid
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Homework Statement


[tex]ac + bc = (a - c)(a + b) - xabcd^2[/tex]

Homework Equations


Various factoring rules (difference of two squares, etc.)

The Attempt at a Solution


I got it expanded to:

[tex]ac + bc = a^2 + ab - ac - bc - xabcd^2\\0 = a^2 + ab - 2ac - bc - bd - xabcd^2[/tex]

I tried factoring different ways, but it didn't really get me anywhere, and there aren't any "special" factoring rules that I can identify immediately here.

Never mind, I wrote down the problem incorrectly
 
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  • #2
PhizKid said:

Homework Statement


[tex]ac + bc = (a - c)(a + b) - xabcd^2[/tex]

Homework Equations


Various factoring rules (difference of two squares, etc.)


The Attempt at a Solution


I got it expanded to:

[tex]ac + bc = a^2 + ab - ac - bc - xabcd^2\\0 = a^2 + ab - 2ac - bc - bd - xabcd^2[/tex]

I tried factoring different ways, but it didn't really get me anywhere, and there aren't any "special" factoring rules that I can identify immediately here.

Never mind, I wrote down the problem incorrectly

Think of this:
What if you were asked to make x the subject (in other words, solve for x by putting it alone on one side of the equation) in the equation

[tex]a=b-cx[/tex]

Can you solve this?
 

1. What is the process for solving an equation with 4 variables and 1 equation?

The process for solving an equation with 4 variables and 1 equation involves isolating the variable you are solving for and manipulating the equation to get the desired variable on one side of the equal sign. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division on both sides of the equation.

2. Can you provide an example of solving an equation with 4 variables and 1 equation?

Yes, an example of solving an equation with 4 variables and 1 equation is:
3x + 2y + 4z + 6w = 24
To solve for x, we can first subtract 2y, 4z, and 6w from both sides to get:
3x = 24 - 2y - 4z - 6w
Then, we can divide both sides by 3 to isolate x:
x = (24 - 2y - 4z - 6w)/3
Therefore, the solution for x is x = (24 - 2y - 4z - 6w)/3.

3. What is the purpose of solving an equation with 4 variables and 1 equation?

The purpose of solving an equation with 4 variables and 1 equation is to find the values of the variables that satisfy the equation. This allows us to solve complex problems and make predictions based on the relationships between the variables.

4. What should I do if I get a negative solution when solving for 'x'?

If you get a negative solution when solving for x, it means that the value of x is a negative number. This may be a valid solution, depending on the context of the problem. If the negative solution does not make sense in the given context, you may need to recheck your calculations or consider if there is a mistake in the original equation.

5. Can you use substitution to solve an equation with 4 variables and 1 equation?

Yes, substitution can be used to solve an equation with 4 variables and 1 equation. This involves solving for one variable in terms of the other three, and then substituting this expression into the original equation to solve for the remaining variable. This method can be used if the equation is not easily solvable using traditional algebraic operations.

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