Which Of The Following Is A True Statement About The Solution To $7x = 28$?A. $x = 2$ Is The Solution To The Equation.B. $ X = 4 X = 4 X = 4 [/tex] Is The Solution To The Equation.C. $x = 5$ Is The Solution To The
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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 simple linear equation, $7x = 28$, and determine which of the given statements is true.
Understanding Linear Equations
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 $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation and graphical methods.
Solving the Equation $7x = 28$
To solve the equation $7x = 28$, we need to isolate the variable $x$. We can do this by dividing both sides of the equation by 7.
Therefore, the solution to the equation $7x = 28$ is $x = 4$.
Evaluating the Given Statements
Now that we have solved the equation, let's evaluate the given statements.
Statement A: $x = 2$ is the solution to the equation.
This statement is false. As we have already seen, the solution to the equation $7x = 28$ is $x = 4$, not $x = 2$.
Statement B: $x = 4$ is the solution to the equation.
This statement is true. We have already seen that the solution to the equation $7x = 28$ is indeed $x = 4$.
Statement C: $x = 5$ is the solution to the equation.
This statement is false. As we have already seen, the solution to the equation $7x = 28$ is $x = 4$, not $x = 5$.
Conclusion
In conclusion, the solution to the equation $7x = 28$ is $x = 4$. Therefore, the correct statement is Statement B: $x = 4$ is the solution to the equation.
Tips and Tricks
- When solving linear equations, always isolate the variable by performing the same operation on both sides of the equation.
- Use inverse operations to solve for the variable. For example, if the equation is $7x = 28$, you can divide both sides by 7 to isolate $x$.
- Check your solution by plugging it back into the original equation.
Real-World Applications
Linear equations have numerous real-world applications, including:
- Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
Common Mistakes
- Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
- Not checking the solution: Failing to check the solution can lead to incorrect answers.
- Not using inverse operations: Failing to use inverse operations can lead to incorrect solutions.
Practice Problems
- Solve the equation $3x = 24$.
- Solve the equation $2x = 16$.
- Solve the equation $x = 5$.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease. Remember to always isolate the variable, use inverse operations, and check your solution. With practice, you will become proficient in solving linear equations and be able to apply them to real-world problems.
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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 $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable by performing the same operation on both sides of the equation. You can use inverse operations to solve for the variable. For example, if the equation is $7x = 28$, you can divide both sides by 7 to isolate $x$.
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, $x = 4$ is a linear equation, while $x^2 = 16$ is a quadratic equation.
Q: Can I use a calculator to solve a linear equation?
A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your solution by plugging it back into the original equation to ensure that it's correct.
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.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not isolating the variable
- Not using inverse operations
- Not checking the solution
- Not simplifying the equation
Q: Can I use linear equations to solve real-world problems?
A: Yes, linear equations can be used to solve real-world problems. For example, you can use linear equations to calculate interest rates, investment returns, and other financial metrics.
Q: What are some examples of real-world applications of linear equations?
A: Some examples of real-world applications of linear equations include:
- Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
Q: How do I practice solving linear equations?
A: You can practice solving linear equations by working through practice problems, such as those found in textbooks or online resources. You can also try solving real-world problems that involve linear equations.
Q: What are some resources for learning more about linear equations?
A: Some resources for learning more about linear equations include:
- Textbooks: There are many textbooks available that cover linear equations in detail.
- Online resources: There are many online resources available that provide tutorials, examples, and practice problems for linear equations.
- Video tutorials: There are many video tutorials available that provide step-by-step instructions for solving linear equations.
Q: Can I use linear equations to solve systems of equations?
A: Yes, linear equations can be used to solve systems of equations. A system of equations is a set of two or more linear equations that are solved simultaneously. You can use substitution or elimination methods to solve systems of equations.
Q: What are some examples of systems of equations?
A: Some examples of systems of equations include:
- Finance: A system of equations can be used to calculate interest rates and investment returns.
- Science: A system of equations can be used to model population growth and chemical reactions.
- Engineering: A system of equations can be used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
Q: How do I solve a system of equations?
A: To solve a system of equations, you can use substitution or elimination methods. Substitution involves solving one equation for one variable and then substituting that expression into the other equation. Elimination involves adding or subtracting the equations to eliminate one variable.
Q: What are some common mistakes to avoid when solving systems of equations?
A: Some common mistakes to avoid when solving systems of equations include:
- Not using substitution or elimination methods
- Not checking the solution
- Not simplifying the equations
- Not using inverse operations
Q: Can I use systems of equations to solve real-world problems?
A: Yes, systems of equations can be used to solve real-world problems. For example, you can use systems of equations to calculate interest rates, investment returns, and other financial metrics.
Q: What are some examples of real-world applications of systems of equations?
A: Some examples of real-world applications of systems of equations include:
- Finance: Systems of equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Systems of equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Systems of equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.