Solve For X X X : 5 ( X − 1 ) = 9 X − 13 5(x - 1) = 9x - 13 5 ( X − 1 ) = 9 X − 13 Simplify Your Answer As Much As Possible. $x = $

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific linear equation, $5(x - 1) = 9x - 13$, 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. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Given Equation

The given equation is $5(x - 1) = 9x - 13$. This equation can be solved using algebraic manipulation, which involves simplifying the equation by combining like terms and isolating the variable.

Step 1: Distribute the 5

To simplify the equation, we need to distribute the 5 to the terms inside the parentheses.

5(x - 1) = 5x - 5

Step 2: Rewrite the Equation

Now that we have distributed the 5, we can rewrite the equation as follows:

5x - 5 = 9x - 13

Step 3: Add 5 to Both Sides

To isolate the variable, we need to add 5 to both sides of the equation.

5x = 9x - 8

Step 4: Subtract 9x from Both Sides

Next, we need to subtract 9x from both sides of the equation to get:

-4x = -8

Step 5: Divide Both Sides by -4

Finally, we need to divide both sides of the equation by -4 to solve for x.

x = 2

Conclusion

In this article, we have solved the linear equation $5(x - 1) = 9x - 13$ using algebraic manipulation. We have distributed the 5, rewritten the equation, added 5 to both sides, subtracted 9x from both sides, and finally divided both sides by -4 to solve for x. The solution to the equation is x = 2.

Tips and Tricks

• When solving linear equations, it is essential to follow the order of operations (PEMDAS) to ensure that the equation is simplified correctly.
• When distributing a coefficient to terms inside parentheses, make sure to multiply each term by the coefficient.
• When adding or subtracting terms, make sure to combine like terms to simplify the equation.
• When dividing both sides of an equation by a coefficient, make sure to check if the coefficient is positive or negative to avoid errors.

Real-World Applications

Linear equations have numerous real-world applications in fields such as physics, engineering, economics, and computer science. Some examples of real-world applications of linear equations include:

• Modeling population growth and decline
• Calculating the cost of goods and services
• Determining the trajectory of projectiles
• Solving systems of linear equations to find the optimal solution

Common Mistakes

When solving linear equations, it is essential to avoid common mistakes such as:

• Not following the order of operations (PEMDAS)
• Not distributing coefficients correctly
• Not combining like terms
• Not checking the sign of the coefficient when dividing both sides of the equation

Conclusion

Introduction

In our previous article, we provided a step-by-step guide on how to solve the linear equation $5(x - 1) = 9x - 13$. In this article, we will answer some frequently asked questions (FAQs) related to solving linear equations.

Q&A

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 the steps outlined in our previous article:

1. Distribute the coefficient to the terms inside the parentheses.
2. Rewrite the equation by combining like terms.
3. Add or subtract the same value to both sides of the equation to isolate the variable.
4. Divide both sides of the equation by the coefficient to solve for the variable.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

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 distribute a coefficient to terms inside parentheses?

A: To distribute a coefficient to terms inside parentheses, you need to multiply each term by the coefficient. For example, if you have the equation $2(x + 3)$, you would distribute the 2 as follows:

$2(x + 3) = 2x + 6$

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, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3 = 5$ is a linear equation.

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

A: Yes, you can use a calculator to solve linear equations. However, it's essential to understand the steps involved in solving the equation and to check your work to ensure that 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 following the order of operations (PEMDAS)
• Not distributing coefficients correctly
• Not combining like terms
• Not checking the sign of the coefficient when dividing both sides of the equation

Conclusion

In conclusion, solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article and avoiding common mistakes, you can become proficient in solving linear equations and apply them to real-world problems. Remember to follow the order of operations (PEMDAS), distribute coefficients correctly, combine like terms, and check the sign of the coefficient when dividing both sides of the equation. With practice and patience, you can become proficient in solving linear equations and achieve your goals.

Additional Resources

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

Final Tips

• Practice solving linear equations regularly to build your skills and confidence.
• Use online resources, such as Khan Academy and Mathway, to supplement your learning.
• Check your work carefully to ensure that the solution is correct.
• Don't be afraid to ask for help if you're struggling with a particular concept or problem.