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

  • MHB
  • Thread starter rynesdad5
  • Start date
  • Tags
    Variables
In summary: There is another fraction in the equation which is (10/3x) so the value of x should be also not zero...so the restriction is x should not be zero...In summary, the equation 5/x=(10/3x)+4 has a solution of x=5/12, but it also has a restriction that x cannot be equal to zero due to the denominator in both fractions. This restriction must be taken into account when solving the equation.
  • #1
rynesdad5
1
0
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.
 
Mathematics news on Phys.org
  • #2
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?
 
  • #3
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
 

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

What are restrictions on variables?

Restrictions on variables refer to limitations or rules that are placed on the values that a variable can take on. These restrictions are usually established in order to ensure that the data being collected or analyzed is accurate and meaningful.

Why are restrictions on variables important in scientific research?

Restrictions on variables are important because they help to control for confounding factors and ensure that the results of a study are valid and reliable. By limiting the range of values that a variable can take on, researchers can better isolate the effects of the independent variable on the dependent variable.

What are some common types of restrictions on variables?

Some common types of restrictions on variables include minimum and maximum values, specific categories or ranges, and exclusion criteria. These restrictions can be applied to both independent and dependent variables.

How do restrictions on variables affect data analysis?

Restrictions on variables can affect data analysis by limiting the range of data that can be included in the analysis. This can lead to more accurate and reliable results, as well as a better understanding of the relationships between variables.

Are there any drawbacks to imposing restrictions on variables in scientific research?

While restrictions on variables can be beneficial, they can also limit the generalizability of a study's findings. If the restrictions are too strict, the results may not be applicable to a larger population. It is important for researchers to carefully consider the potential drawbacks of restrictions on variables when designing a study.

Similar threads

B Solving the Heart Curve Equation: 'y =
Replies
18
Views
3K
MHB Solve System of Inequalities: 2x+3y-4, 3x-4y+5
Replies
8
Views
1K
MHB Quadratic equations ( solving for zeros/roots) trickey
Replies
1
Views
1K
MHB How to Solve These Math Equations for x?
Replies
1
Views
2K
MHB Fixed point,, Jacobi- & Newton Method, Linear Systems
Replies
7
Views
2K
MHB Logarithmic Equation solve log_(3x)3+log_(x/3)3=5/12
Replies
1
Views
1K
MHB Solve √(x^2+3x+7)-√(x^2-3x+9)+2=0
Replies
5
Views
2K
MHB Connectors between lines of working
Replies
8
Views
3K
MHB Simplify and state any restrictions on the variables.
Replies
2
Views
2K
MHB Solve Exponential Equation 4^(5-9x)=1/(8^(x-2) )
Replies
7
Views
3K

Hot Threads

Recent Insights

Back
Top