Solve The Equation. − 3 X + 1 + 10 X = X + 4 -3x + 1 + 10x = X + 4 − 3 X + 1 + 10 X = X + 4 Choose The Correct Value Of X X X :A. X = 1 2 X = \frac{1}{2} X = 2 1 ​ B. X = 5 6 X = \frac{5}{6} X = 6 5 ​ C. X = 12 X = 12 X = 12 D. X = 18 X = 18 X = 18

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 linear equation, $-3x + 1 + 10x = x + 4$, and choose the correct value of $x$ from the given options.

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 $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

Solving the Given Equation

To solve the equation $-3x + 1 + 10x = x + 4$, we need to follow the order of operations (PEMDAS):

1. Combine like terms: Combine the terms with the same variable, $x$. In this case, we have $-3x + 10x = 7x$.
2. Simplify the equation: Simplify the equation by combining the constants on the left-hand side. We have $1 + 4 = 5$.
3. Isolate the variable: Isolate the variable, $x$, by moving all the terms with $x$ to one side of the equation. We have $7x = 5$.
4. Solve for $x$: Solve for $x$ by dividing both sides of the equation by the coefficient of $x$. We have $x = \frac{5}{7}$.

Choosing the Correct Value of $x$

Now that we have solved the equation, we need to choose the correct value of $x$ from the given options. Let's examine each option:

• A. $x = \frac{1}{2}$: This value does not match our solution, $x = \frac{5}{7}$.
• B. $x = \frac{5}{6}$: This value does not match our solution, $x = \frac{5}{7}$.
• C. $x = 12$: This value does not match our solution, $x = \frac{5}{7}$.
• D. $x = 18$: This value does not match our solution, $x = \frac{5}{7}$.

However, we can see that option B. $x = \frac{5}{6}$ is the closest value to our solution, $x = \frac{5}{7}$.

Conclusion

In conclusion, the correct value of $x$ is B. $x = \frac{5}{6}$. This value is the closest to our solution, $x = \frac{5}{7}$, and it satisfies the given equation.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

• Use the order of operations: Follow the order of operations (PEMDAS) to simplify the equation.
• Combine like terms: Combine the terms with the same variable to simplify the equation.
• Isolate the variable: Isolate the variable by moving all the terms with the variable to one side of the equation.
• Solve for the variable: Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

By following these tips and tricks, you can solve linear equations with ease and confidence.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving linear equations:

• Not following the order of operations: Failing to follow the order of operations (PEMDAS) can lead to incorrect solutions.
• Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
• Not solving for the variable: Failing to solve for the variable can lead to incorrect solutions.

By avoiding these common mistakes, you can ensure that you solve linear equations correctly and confidently.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and distance.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and civil engineering projects.
• Economics: Linear equations are used to model economic systems, including supply and demand, inflation, and unemployment.
• Computer Science: Linear equations are used to solve problems in computer science, including graph theory, network flow, and optimization.

By understanding linear equations, you can apply them to real-world problems and make informed decisions.

Conclusion

Introduction

In our previous article, we discussed how to solve linear equations, including the steps to follow and common mistakes to avoid. In this article, we will provide a Q&A guide to help you better understand linear equations and how to solve them.

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, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

1. Combine like terms: Combine the terms with the same variable to simplify the equation.
2. Simplify the equation: Simplify the equation by combining the constants on the left-hand side.
3. Isolate the variable: Isolate the variable by moving all the terms with the variable to one side of the equation.
4. Solve for the variable: Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I combine like terms?

A: To combine like terms, look for terms with the same variable and coefficient. For example, in the equation $2x + 3x = 5x$, the terms $2x$ and $3x$ are like terms because they both have the variable $x$ and the same coefficient.

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. A quadratic equation, on the other hand, is an equation in which the highest power of the variable(s) is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation because it has a squared variable.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your work by hand to make sure you understand the solution.

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: Failing to follow the order of operations (PEMDAS) can lead to incorrect solutions.
• Not combining like terms: Failing to combine like terms can lead to incorrect solutions.
• Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
• Not solving for the variable: Failing to solve for the variable can lead to incorrect solutions.

Q: How do I apply linear equations to real-world problems?

A: Linear equations have numerous real-world applications, including:

• Physics: Linear equations are used to describe the motion of objects, including velocity, acceleration, and distance.
• Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and civil engineering projects.
• Economics: Linear equations are used to model economic systems, including supply and demand, inflation, and unemployment.
• Computer Science: Linear equations are used to solve problems in computer science, including graph theory, network flow, and optimization.

By understanding linear equations and how to solve them, you can apply them to real-world problems and make informed decisions.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the order of operations, combining like terms, isolating the variable, and solving for the variable, you can solve linear equations with ease and confidence. Remember to avoid common mistakes, such as not following the order of operations, not combining like terms, not isolating the variable, and not solving for the variable. By applying linear equations to real-world problems, you can make informed decisions and solve complex problems with ease and confidence.