To Solve $\frac{x}{20}+\frac{4}{5}=2$, Let's Multiply Both Sides Of The Equation By 20. Once This Is Done, Identify The Equivalent Equation.Choose The Correct Answer Below:A. $x+4=2$B. $x+16=22$C. $x+16=40$D.
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific type of linear equation, which involves multiplying both sides of the equation by a constant. We will use a step-by-step approach to solve the equation and identify the equivalent equation.
Understanding the Problem
The given equation is . Our goal is to solve for the variable . To do this, we need to isolate the variable on one side of the equation.
Step 1: Multiply Both Sides by 20
To eliminate the fractions, we can multiply both sides of the equation by 20. This will allow us to work with whole numbers and make it easier to solve for .
\frac{x}{20}+\frac{4}{5}=2
\implies 20\left(\frac{x}{20}+\frac{4}{5}\right)=20(2)
\implies x+16=40
Step 2: Simplify the Equation
After multiplying both sides by 20, we get the equation . This equation is now in a simpler form, and we can easily solve for .
Step 3: Solve for
To solve for , we need to isolate the variable on one side of the equation. We can do this by subtracting 16 from both sides of the equation.
x+16=40
\implies x+16-16=40-16
\implies x=24
Conclusion
In this article, we solved the linear equation by multiplying both sides by 20 and then simplifying the equation. We found that the equivalent equation is , and by solving for , we found that . This demonstrates the importance of following the order of operations and simplifying equations to solve for variables.
Answer
The correct answer is:
C.
Discussion
This problem is a great example of how to solve linear equations by multiplying both sides by a constant. By following the steps outlined in this article, students can develop a deeper understanding of how to solve linear equations and become more confident in their math skills.
Common Mistakes
When solving linear equations, students often make mistakes by not following the order of operations or by not simplifying the equation. To avoid these mistakes, students should:
- Follow the order of operations (PEMDAS)
- Simplify the equation by combining like terms
- Check their work by plugging in the solution back into the original equation
Real-World Applications
Solving linear equations has many real-world applications, such as:
- Finance: Solving linear equations can help individuals calculate interest rates, investments, and loans.
- Science: Solving linear equations can help scientists model population growth, chemical reactions, and other phenomena.
- Engineering: Solving linear equations can help engineers design and optimize systems, such as bridges, buildings, and electronic circuits.
Conclusion
Introduction
In our previous article, we discussed how to solve linear equations by multiplying both sides by a constant. In this article, we will provide a Q&A guide to help students better understand the concept of solving linear equations.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants.
Q: How do I know if an equation is linear?
A: To determine if an equation is linear, look for the following characteristics:
- The highest power of the variable(s) is 1.
- The equation can be written in the form ax + b = c, where a, b, and c are constants.
- The equation does not contain any exponents or roots.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when working with mathematical expressions. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an equation?
A: To simplify an equation, combine like terms and eliminate any unnecessary operations. For example, if you have the equation 2x + 3x = 5, you can simplify it by combining the like terms: 5x = 5.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation x + 2 = 3 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I solve a linear equation with fractions?
A: To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators. For example, if you have the equation 1/2x + 1/4 = 3/4, you can multiply both sides by 4 to eliminate the fractions: 2x + 1 = 3.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not following the order of operations
- Not simplifying the equation
- Not checking the solution by plugging it back into the original equation
- Not considering the possibility of multiple solutions
Q: How do I check my solution to a linear equation?
A: To check your solution to a linear equation, plug the solution back into the original equation and simplify. If the equation is true, then your solution is correct. If the equation is false, then your solution is incorrect.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, students can develop a deeper understanding of how to solve linear equations and become more confident in their math skills. Whether it's in finance, science, or engineering, solving linear equations has many real-world applications that can help individuals make informed decisions and solve complex problems.