Solve For $x$.$17 = \frac{x}{5} - 16$Simplify Your Answer As Much As Possible. $ X = X = X = [/tex]
In mathematics, solving for x in a linear equation is a fundamental concept that involves isolating the variable x on one side of the equation. This is a crucial skill that is used extensively in various branches of mathematics, including algebra, geometry, and calculus. In this article, we will focus on solving for x in a linear equation of the form ax = b, where a and b are constants.
Understanding the Equation
The given equation is 17 = x/5 - 16. To solve for x, we need to isolate x on one side of the equation. The first step is to simplify the equation by getting rid of the fraction. We can do this by multiplying both sides of the equation by 5, which is the denominator of the fraction.
Multiplying Both Sides by 5
Multiplying both sides of the equation by 5 gives us:
5(17) = 5(x/5 - 16)
This simplifies to:
85 = x - 80
Adding 80 to Both Sides
The next step is to add 80 to both sides of the equation to get rid of the negative term. This gives us:
85 + 80 = x
Simplifying the Equation
Simplifying the equation gives us:
165 = x
Conclusion
In conclusion, solving for x in a linear equation involves isolating the variable x on one side of the equation. We can do this by simplifying the equation, multiplying both sides by a constant, and adding or subtracting a constant from both sides. In this article, we solved for x in the equation 17 = x/5 - 16 and found that x = 165.
Real-World Applications
Solving for x in a linear equation has numerous real-world applications. For example, in physics, we can use linear equations to model the motion of objects. In economics, we can use linear equations to model the relationship between two variables. In engineering, we can use linear equations to design and optimize systems.
Tips and Tricks
Here are some tips and tricks to help you solve for x in a linear equation:
- Make sure to simplify the equation before solving for x.
- Use the distributive property to multiply both sides of the equation by a constant.
- Add or subtract a constant from both sides of the equation to get rid of a negative term.
- Check your solution by plugging it back into the original equation.
Common Mistakes
Here are some common mistakes to avoid when solving for x in a linear equation:
- Failing to simplify the equation before solving for x.
- Multiplying both sides of the equation by a constant without checking if it is a factor of the equation.
- Adding or subtracting a constant from both sides of the equation without checking if it is a factor of the equation.
- Not checking your solution by plugging it back into the original equation.
Conclusion
In our previous article, we discussed how to solve for x in a linear equation. However, we know that practice makes perfect, and there's no better way to practice than by answering questions. In this article, we'll provide a Q&A section to help you reinforce your understanding of solving for x in a linear equation.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable (x) is 1. It can be written in the form ax = b, where a and b are constants.
Q: How do I solve for x in a linear equation?
A: To solve for x in a linear equation, you need to isolate the variable x on one side of the equation. You can do this by simplifying the equation, multiplying both sides by a constant, and adding or subtracting a constant from both sides.
Q: What is the first step in solving for x in a linear equation?
A: The first step in solving for x in a linear equation is to simplify the equation. This involves getting rid of any fractions or decimals by multiplying both sides of the equation by a constant.
Q: How do I multiply both sides of the equation by a constant?
A: To multiply both sides of the equation by a constant, you need to multiply each term on both sides of the equation by the constant. For example, if the equation is 2x = 5, and you want to multiply both sides by 3, you would get 6x = 15.
Q: What is the next step in solving for x in a linear equation?
A: The next step in solving for x in a linear equation is to add or subtract a constant from both sides of the equation. This involves getting rid of any negative terms by adding a constant to both sides of the equation.
Q: How do I add or subtract a constant from both sides of the equation?
A: To add or subtract a constant from both sides of the equation, you need to add or subtract the constant from each term on both sides of the equation. For example, if the equation is x - 3 = 2, and you want to add 3 to both sides, you would get x = 5.
Q: What is the final step in solving for x in a linear equation?
A: The final step in solving for x in a linear equation is to check your solution by plugging it back into the original equation. This ensures that your solution is correct and satisfies the original equation.
Q: What are some common mistakes to avoid when solving for x in a linear equation?
A: Some common mistakes to avoid when solving for x in a linear equation include:
- Failing to simplify the equation before solving for x.
- Multiplying both sides of the equation by a constant without checking if it is a factor of the equation.
- Adding or subtracting a constant from both sides of the equation without checking if it is a factor of the equation.
- Not checking your solution by plugging it back into the original equation.
Q: How can I practice solving for x in a linear equation?
A: You can practice solving for x in a linear equation by working through a series of problems. You can find practice problems in your textbook or online. You can also try solving for x in a linear equation by creating your own problems.
Q: What are some real-world applications of solving for x in a linear equation?
A: Solving for x in a linear equation has numerous real-world applications. For example, in physics, we can use linear equations to model the motion of objects. In economics, we can use linear equations to model the relationship between two variables. In engineering, we can use linear equations to design and optimize systems.
Conclusion
In conclusion, solving for x in a linear equation is a fundamental concept in mathematics that involves isolating the variable x on one side of the equation. By following the steps outlined in this article, you can become proficient in solving for x in a linear equation. Remember to practice regularly and avoid common mistakes to ensure that you are solving for x correctly.