If $f(x) = \frac{x}{2} + 8$, What Is $f(x)$ When $ X = 10 X = 10 X = 10 [/tex]?A. 4 B. 9 C. 13 D. 36
Understanding the Problem
When given a function and a specific value for the variable, we need to find the corresponding value of the function. In this case, we are given the function $f(x) = \frac{x}{2} + 8$ and we need to find $f(x)$ when $x = 10$. This is a simple linear equation, and we can solve it by substituting the given value of $x$ into the function.
Substituting the Value of x
To find $f(x)$ when $x = 10$, we need to substitute $x = 10$ into the function $f(x) = \frac{x}{2} + 8$. This means we replace every instance of $x$ with $10$.
Solving the Equation
Now that we have substituted $x = 10$ into the function, we can solve for $f(x)$. We have:
Conclusion
Therefore, when $x = 10$, $f(x) = 13$. This means that the correct answer is C. 13.
Why is this Important?
Understanding how to solve simple linear equations like this one is crucial in mathematics and real-world applications. It helps us to model and analyze real-world situations, make predictions, and solve problems. In this case, we can use this equation to model a situation where we need to find the value of a function when a specific value of the variable is given.
Real-World Applications
This type of equation has many real-world applications, such as:
- Finance: Understanding how to solve simple linear equations can help us to model and analyze financial situations, such as calculating interest rates or investment returns.
- Science: Simple linear equations can be used to model and analyze scientific phenomena, such as the motion of objects or the growth of populations.
- Engineering: Engineers use simple linear equations to design and optimize systems, such as bridges or electronic circuits.
Tips and Tricks
Here are some tips and tricks to help you solve simple linear equations like this one:
- Read the problem carefully: Make sure you understand what the problem is asking for.
- Substitute the value of x: Replace every instance of $x$ with the given value.
- Simplify the equation: Combine like terms and simplify the equation as much as possible.
- Check your answer: Make sure your answer makes sense in the context of the problem.
Common Mistakes
Here are some common mistakes to avoid when solving simple linear equations like this one:
- Not reading the problem carefully: Make sure you understand what the problem is asking for.
- Not substituting the value of x: Replace every instance of $x$ with the given value.
- Not simplifying the equation: Combine like terms and simplify the equation as much as possible.
- Not checking your answer: Make sure your answer makes sense in the context of the problem.
Conclusion
In conclusion, solving simple linear equations like this one is a crucial skill in mathematics and real-world applications. By following the steps outlined in this article, you can solve simple linear equations with ease and confidence. Remember to read the problem carefully, substitute the value of x, simplify the equation, and check your answer. With practice and patience, you can become proficient in solving simple linear equations and apply them to real-world situations.
Q: What is a simple linear equation?
A: A simple linear equation is an equation that can be written in the form $f(x) = mx + b$, where $m$ and $b$ are constants. It is called "simple" because it has a linear relationship between the variable $x$ and the function $f(x)$.
Q: How do I solve a simple linear equation?
A: To solve a simple linear equation, you need to substitute the given value of $x$ into the function and simplify the equation. This will give you the value of $f(x)$.
Q: What if the equation is in the form $f(x) = \frac{x}{a} + b$?
A: If the equation is in the form $f(x) = \frac{x}{a} + b$, you can still solve it by substituting the given value of $x$ into the function and simplifying the equation. Just remember to multiply the fraction by the reciprocal of the denominator to get rid of the fraction.
Q: What if I have a fraction in the equation?
A: If you have a fraction in the equation, you can simplify it by multiplying the numerator and denominator by the same value. This will get rid of the fraction and make it easier to solve.
Q: How do I check my answer?
A: To check your answer, plug the value of $x$ back into the original equation and make sure it is true. If it is true, then your answer is correct.
Q: What if I get a negative answer?
A: If you get a negative answer, it is still a valid solution. Just make sure you understand the context of the problem and whether a negative answer makes sense.
Q: Can I use a calculator to solve simple linear equations?
A: Yes, you can use a calculator to solve simple linear equations. However, make sure you understand the steps involved in solving the equation and can explain your answer.
Q: What if I have a system of linear equations?
A: If you have a system of linear equations, you can solve it by using substitution or elimination methods. These methods involve solving one equation for one variable and then substituting that value into the other equation.
Q: Can I use a graphing calculator to solve simple linear equations?
A: Yes, you can use a graphing calculator to solve simple linear equations. Graphing calculators can help you visualize the relationship between the variable and the function, and can also be used to find the value of the function at a specific point.
Q: What if I have a quadratic equation?
A: If you have a quadratic equation, you can solve it by using the quadratic formula or factoring. The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, and factoring involves finding two binomials whose product is the original equation.
Q: Can I use a calculator to solve quadratic equations?
A: Yes, you can use a calculator to solve quadratic equations. However, make sure you understand the steps involved in solving the equation and can explain your answer.
Q: What if I have a system of quadratic equations?
A: If you have a system of quadratic equations, you can solve it by using substitution or elimination methods. These methods involve solving one equation for one variable and then substituting that value into the other equation.
Conclusion
In conclusion, solving simple linear equations is a crucial skill in mathematics and real-world applications. By following the steps outlined in this article, you can solve simple linear equations with ease and confidence. Remember to read the problem carefully, substitute the value of x, simplify the equation, and check your answer. With practice and patience, you can become proficient in solving simple linear equations and apply them to real-world situations.