What Is The Solution To This Equation? 7 X − 2 ( X − 10 ) = 40 7x - 2(x - 10) = 40 7 X − 2 ( X − 10 ) = 40 A. X = 6 X = 6 X = 6 B. X = 4 X = 4 X = 4 C. X = 10 X = 10 X = 10 D. X = 12 X = 12 X = 12

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Introduction

In mathematics, solving equations is a fundamental concept that helps us understand the relationship between variables and constants. Equations are used to represent real-world problems, and solving them is essential to find the value of unknown variables. In this article, we will focus on solving a linear equation, $7x - 2(x - 10) = 40$, and find the solution.

Understanding the Equation

The given equation is a linear equation, which means it is an equation in which the highest power of the variable (in this case, $x$) is 1. The equation is $7x - 2(x - 10) = 40$. To solve this equation, we need to isolate the variable $x$.

Distributive Property

To simplify the equation, we can use the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. We can apply this property to the equation by distributing the $-2$ to the terms inside the parentheses.

7x - 2(x - 10) = 40
7x - 2x + 20 = 40

Combining Like Terms

Now that we have simplified the equation, we can combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms, $7x$ and $-2x$, which can be combined as follows:

7x - 2x + 20 = 40
5x + 20 = 40

Isolating the Variable

Now that we have combined like terms, we can isolate the variable $x$ by subtracting 20 from both sides of the equation.

5x + 20 = 40
5x = 20

Solving for $x$

Finally, we can solve for $x$ by dividing both sides of the equation by 5.

5x = 20
x = 20/5
x = 4

Conclusion

In this article, we solved the linear equation $7x - 2(x - 10) = 40$ and found the solution to be $x = 4$. We used the distributive property to simplify the equation, combined like terms, and isolated the variable $x$ to find the solution.

Final Answer

The final answer to the equation $7x - 2(x - 10) = 40$ is $x = 4$.

Discussion

The solution to this equation is $x = 4$. This means that when we substitute $x = 4$ into the original equation, the equation holds true.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Simplify the equation using the distributive property.
2. Combine like terms.
3. Isolate the variable $x$ by subtracting 20 from both sides of the equation.
4. Solve for $x$ by dividing both sides of the equation by 5.

Common Mistakes

When solving this equation, some common mistakes to avoid are:

• Not using the distributive property to simplify the equation.
• Not combining like terms.
• Not isolating the variable $x$ correctly.
• Not solving for $x$ correctly.

Real-World Applications

This equation has many real-world applications, such as:

• Finding the value of a variable in a linear equation.
• Solving systems of linear equations.
• Modeling real-world problems using linear equations.

Conclusion

In conclusion, solving the linear equation $7x - 2(x - 10) = 40$ requires careful application of mathematical concepts, such as the distributive property, combining like terms, and isolating the variable $x$. By following these steps, we can find the solution to the equation and apply it to real-world problems.

Introduction

In our previous article, we solved the linear equation $7x - 2(x - 10) = 40$ and found the solution to be $x = 4$. In this article, we will answer some frequently asked questions (FAQs) about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. It is used to simplify equations by distributing the terms inside the parentheses.

Q: How do I combine like terms?

A: Like terms are terms that have the same variable raised to the same power. To combine like terms, simply add or subtract the coefficients of the terms. For example, $2x + 3x = 5x$.

Q: How do I isolate the variable?

A: To isolate the variable, you need to get the variable by itself on one side of the equation. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

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 solving an equation. 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 solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to find the values of the variables that satisfy both equations. This can be done using substitution or elimination methods.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

• Not using the distributive property to simplify the equation.
• Not combining like terms.
• Not isolating the variable correctly.
• Not solving for the variable correctly.
• Not checking the solution by plugging it back into the original equation.

Q: How do I check my solution?

A: To check your solution, plug the value of the variable back into the original equation and simplify. If the equation holds true, then your solution is correct.

Conclusion

In conclusion, solving linear equations requires careful application of mathematical concepts, such as the distributive property, combining like terms, and isolating the variable. By following these steps and avoiding common mistakes, you can solve linear equations and apply them to real-world problems.

Final Tips

• Always check your solution by plugging it back into the original equation.
• Use the distributive property to simplify equations.
• Combine like terms to simplify equations.
• Isolate the variable to find the solution.
• Use the order of operations to evaluate expressions.
• Eliminate fractions by multiplying both sides of the equation by the LCM of the denominators.

Resources

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Discussion

The solution to this equation is $x = 4$. This means that when we substitute $x = 4$ into the original equation, the equation holds true.

Step-by-Step Solution

Here is the step-by-step solution to the equation:

1. Simplify the equation using the distributive property.
2. Combine like terms.
3. Isolate the variable $x$ by subtracting 20 from both sides of the equation.
4. Solve for $x$ by dividing both sides of the equation by 5.

Common Mistakes

When solving this equation, some common mistakes to avoid are:

• Not using the distributive property to simplify the equation.
• Not combining like terms.
• Not isolating the variable $x$ correctly.
• Not solving for $x$ correctly.

Real-World Applications

This equation has many real-world applications, such as:

• Finding the value of a variable in a linear equation.
• Solving systems of linear equations.
• Modeling real-world problems using linear equations.

Conclusion

In conclusion, solving linear equations requires careful application of mathematical concepts, such as the distributive property, combining like terms, and isolating the variable. By following these steps and avoiding common mistakes, you can solve linear equations and apply them to real-world problems.