MHB What Are the Variable Restrictions in the Equation 5/x = (10/3x) + 4?

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The equation 5/x = (10/3x) + 4 has variable restrictions due to the denominators, which cannot be zero. Specifically, x cannot equal zero and x cannot equal zero from the second fraction, meaning x must be greater than zero. The solution to the equation is x = 5/12, which is valid under these restrictions. It's important to ensure that any solution does not violate the restrictions set by the denominators. Therefore, the final answer is valid as it adheres to the necessary conditions.
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Write the restrictions on the variables for the following equation. Keeping in mind the restrictions, solve the equation

5/x=(10/3x)+4

Here is what I did, but I'm not sure if it's right.

(3x)(5/x)=(3x)[(10/3x)+4]

15=(3x)(10/3x)+(3x)4

15=10+12x

5=12x

x=5/12

But I don't know what to do about the restrictions. Can someone help? Thank you in advance.
 
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Hi rynesdad5,:)

Welcome to MHB!

You've solved the problem correctly but you have to keep in mind that the denominator of any fraction cannot be zero. If the denominator is zero, then the expression is not real because its overall value is undefined, since, e.g. $\dfrac{2}{0}=\infty$.

In your problem, you have two fractions there, one is $\dfrac{5}{x}$ and the other is $\dfrac{10}{3x}$. What can you say about the value(s) of $x$ that you couldn't take for these two fractions?
 
rynesdad5 said:
Write the restrictions on the variables for the following equation. Keeping in mind the restrictions, solve the equation

5/x=(10/3x)+4

Here is what I did, but I'm not sure if it's right.

(3x)(5/x)=(3x)[(10/3x)+4]

15=(3x)(10/3x)+(3x)4

15=10+12x

5=12x

x=5/12

But I don't know what to do about the restrictions. Can someone help? Thank you in advance.

I think you have solved the problem correctly..If x is in denominator itself you should take care of x,it should not be zero
 
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