The Given Equation Has Been Solved In The Table Below.$\[ \begin{tabular}{|c|c|} \hline Step & Statement \\ \hline 1 & $-7n + 11 = -10$ \\ \hline 2 & $-7n + 11 - 11 = -10 - 11$ \\ \hline 3 & $-7n = -21$ \\ \hline 4 & $\frac{-7n}{-7} =

The Given Equation Has Been Solved in the Table Below

The given equation has been solved in the table below, and in this article, we will discuss the step-by-step solution to the equation. The equation provided is ${-7n + 11 = -10}$. Our goal is to isolate the variable $n$ and find its value.

Step 1: Simplify the Equation

The first step in solving the equation is to simplify it by performing the necessary operations. In this case, we need to isolate the term with the variable $n$. To do this, we can subtract $11$ from both sides of the equation.

$${-7n + 11 - 11 = -10 - 11}$$

This simplifies to:

$${-7n = -21}$$

Step 2: Solve for the Variable

Now that we have isolated the term with the variable $n$, we can solve for $n$ by dividing both sides of the equation by $-7$.

$${\frac{-7n}{-7} = \frac{-21}{-7}}$$

This simplifies to:

$${n = 3}$$

Conclusion

In conclusion, the given equation has been solved in the table below, and we have found the value of the variable $n$ to be $3$. The step-by-step solution to the equation is as follows:

1. Simplify the equation by subtracting $11$ from both sides.
2. Isolate the term with the variable $n$ by dividing both sides of the equation by $-7$.

By following these steps, we can solve for the variable $n$ and find its value.

Discussion

The given equation is a linear equation in one variable, and it can be solved using basic algebraic operations. The equation is in the form of $ax + b = c$, where $a$, $b$, and $c$ are constants. To solve for the variable $x$, we need to isolate the term with the variable by performing the necessary operations.

In this case, we subtracted $11$ from both sides of the equation to simplify it, and then we divided both sides of the equation by $-7$ to isolate the term with the variable $n$. This resulted in the value of $n$ being $3$.

Importance of Solving Linear Equations

Solving linear equations is an important skill in mathematics, and it has many practical applications in real-life situations. For example, in physics, linear equations are used to describe the motion of objects, and in economics, linear equations are used to model the behavior of economic systems.

In addition, solving linear equations helps to develop problem-solving skills, critical thinking skills, and analytical skills. It also helps to build confidence in mathematics and prepares students for more advanced mathematical concepts.

Tips for Solving Linear Equations

Here are some tips for solving linear equations:

1. Read the equation carefully: Before solving the equation, read it carefully to understand what is being asked.
2. Simplify the equation: Simplify the equation by performing the necessary operations, such as adding or subtracting the same value to both sides.
3. Isolate the term with the variable: Isolate the term with the variable by performing the necessary operations, such as dividing both sides of the equation by a constant.
4. Check the solution: Check the solution by plugging it back into the original equation to ensure that it is true.

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

Conclusion

In conclusion, the given equation has been solved in the table below, and we have found the value of the variable $n$ to be $3$. The step-by-step solution to the equation is as follows:

1. Simplify the equation by subtracting $11$ from both sides.
2. Isolate the term with the variable $n$ by dividing both sides of the equation by $-7$.

By following these steps, we can solve for the variable $n$ and find its value. Solving linear equations is an important skill in mathematics, and it has many practical applications in real-life situations.
Frequently Asked Questions (FAQs) About Solving Linear Equations

In this article, we will answer some frequently asked questions about solving linear equations. If you have any questions or need further clarification, feel free to ask.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the term with the variable by performing the necessary operations, such as adding or subtracting the same value to both sides, or dividing both sides of the equation by a constant.

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. Quadratic equations are more complex and require more advanced algebraic operations to solve.

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 is always a good idea to check the solution by plugging it back into the original equation to ensure that it is true.

Q: How do I check the solution to a linear equation?

A: To check the solution to a linear equation, plug the solution back into the original equation and simplify. If the equation is true, then the 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 reading the equation carefully before solving it
• Not simplifying the equation before solving it
• Not isolating the term with the variable before solving it
• Not checking the solution before accepting it as correct

Q: Can I use algebraic properties to solve linear equations?

A: Yes, you can use algebraic properties to solve linear equations. For example, you can use the commutative property of addition to rearrange the terms in the equation, or the distributive property of multiplication to expand the equation.

Q: How do I use algebraic properties to solve linear equations?

A: To use algebraic properties to solve linear equations, identify the property that can be used to simplify the equation, and then apply it to the equation. For example, if the equation is $2x + 3 = 5$, you can use the commutative property of addition to rearrange the terms as $3 + 2x = 5$.

Q: Can I use real-world examples to solve linear equations?

A: Yes, you can use real-world examples to solve linear equations. For example, if you are given the equation $x + 2 = 5$, you can use a real-world example, such as a problem involving the cost of an item, to solve the equation.

Conclusion

In conclusion, solving linear equations is an important skill in mathematics, and it has many practical applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease and confidence. Remember to read the equation carefully, simplify the equation, isolate the term with the variable, and check the solution before accepting it as correct.