Solve For $x$.$15x - 6x = 63$Simplify Your Answer As Much As Possible.$ X = X = X = [/tex]

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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 specific linear equation, $15x - 6x = 63$, and provide a step-by-step guide on how to simplify the solution.

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.

Solving the Linear Equation

To solve the linear equation $15x - 6x = 63$, we need to follow these steps:

Step 1: Combine Like Terms

The first step is to combine like terms on the left-hand side of the equation. In this case, we have two terms with the variable $x$, which are $15x$ and $-6x$. We can combine these terms by adding or subtracting their coefficients.

# Import necessary modules
import sympy as sp

x = sp.symbols('x')



equation = 15x - 6x - 63



simplified_equation = sp.simplify(equation)

Step 2: Isolate the Variable

Once we have combined like terms, we need to isolate the variable $x$ on one side of the equation. In this case, we can do this by adding $6x$ to both sides of the equation.

# Isolate the variable
isolated_variable = sp.Eq(simplified_equation, 63)

Step 3: Solve for x

Now that we have isolated the variable $x$, we can solve for its value. In this case, we can do this by dividing both sides of the equation by the coefficient of $x$, which is $9$.

# Solve for x
solution = sp.solve(isolated_variable, x)

Simplifying the Solution

Once we have solved for $x$, we need to simplify the solution. In this case, we can do this by evaluating the expression $\frac{63}{9}$.

# Simplify the solution
simplified_solution = solution[0]

Conclusion

In this article, we have solved the linear equation $15x - 6x = 63$ using a step-by-step approach. We have combined like terms, isolated the variable $x$, and solved for its value. Finally, we have simplified the solution to obtain the final answer.

Final Answer

The final answer is: 7\boxed{7}

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Introduction

In our previous article, we solved the linear equation $15x - 6x = 63$ using a step-by-step approach. In this article, we will provide a Q&A guide to help students understand the concepts and techniques involved in solving linear equations.

Q&A: 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, and $x$ is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to follow these steps:

  1. Combine like terms on the left-hand side of the equation.
  2. Isolate the variable on one side of the equation.
  3. Solve for the value of the variable.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. For example, if you have the equation $2x + 5x = 7$, you can combine the like terms by adding their coefficients: $2x + 5x = 7x$.

Q: How do I isolate the variable?

A: To isolate the variable, you need to get it by itself on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation. For example, if you have the equation $2x + 3 = 7$, you can isolate the variable by subtracting 3 from both sides: $2x = 7 - 3$.

Q: How do I solve for the value of the variable?

A: To solve for the value of the variable, you need to divide both sides of the equation by the coefficient of the variable. For example, if you have the equation $2x = 7$, you can solve for the value of $x$ by dividing both sides by 2: $x = \frac{7}{2}$.

Common Mistakes to Avoid

Mistake 1: Not combining like terms

A: Failing to combine like terms can lead to incorrect solutions. Make sure to combine like terms on the left-hand side of the equation.

Mistake 2: Not isolating the variable

A: Failing to isolate the variable can lead to incorrect solutions. Make sure to isolate the variable on one side of the equation.

Mistake 3: Not solving for the value of the variable

A: Failing to solve for the value of the variable can lead to incorrect solutions. Make sure to solve for the value of the variable by dividing both sides of the equation by the coefficient of the variable.

Conclusion

In this article, we have provided a Q&A guide to help students understand the concepts and techniques involved in solving linear equations. We have covered topics such as combining like terms, isolating the variable, and solving for the value of the variable. By following these steps and avoiding common mistakes, students can become proficient in solving linear equations.

Final Tips

Tip 1: Practice, practice, practice!

A: The more you practice solving linear equations, the more comfortable you will become with the concepts and techniques involved.

Tip 2: Use online resources

A: There are many online resources available that can help you practice solving linear equations, such as online calculators and interactive math games.

Tip 3: Seek help when needed

A: Don't be afraid to ask for help if you are struggling with a particular concept or technique. Your teacher, tutor, or classmate may be able to provide additional support and guidance.