Solve For $c$.$5c + 16.5 = 13.5 + 10c$

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, $5c + 16.5 = 13.5 + 10c$, to demonstrate the step-by-step process involved.

Understanding the Equation

The given equation is a linear equation in one variable, $c$. The equation is in the form of $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants. In this case, $a = 5$, $b = 16.5$, $c = 10$, and $d = 13.5$.

Step 1: Isolate the Variable

To solve for $c$, we need to isolate the variable on one side of the equation. We can start by subtracting $10c$ from both sides of the equation.

5c + 16.5 = 13.5 + 10c
5c - 10c + 16.5 = 13.5
-5c + 16.5 = 13.5

Step 2: Simplify the Equation

Next, we can simplify the equation by combining like terms.

-5c + 16.5 = 13.5
-5c = 13.5 - 16.5
-5c = -3

Step 3: Solve for the Variable

Now, we can solve for $c$ by dividing both sides of the equation by $-5$.

-5c = -3
c = -3 / -5
c = 0.6

Conclusion

In this article, we solved a linear equation, $5c + 16.5 = 13.5 + 10c$, to demonstrate the step-by-step process involved. By isolating the variable, simplifying the equation, and solving for the variable, we arrived at the solution, $c = 0.6$. This example illustrates the importance of following a systematic approach when solving linear equations.

Tips and Tricks

• When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure accuracy.
• Isolating the variable on one side of the equation is a crucial step in solving linear equations.
• Simplifying the equation by combining like terms can make it easier to solve for the variable.

Real-World Applications

Linear equations have numerous real-world applications, including:

• Finance: Linear equations are used to calculate interest rates, investment returns, and loan payments.
• Science: Linear equations are used to model population growth, chemical reactions, and physical systems.
• Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.

Common Mistakes to Avoid

When solving linear equations, it's essential to avoid common mistakes, including:

• Not following the order of operations (PEMDAS)
• Not isolating the variable on one side of the equation
• Not simplifying the equation by combining like terms

Conclusion

Introduction

In our previous article, we discussed the step-by-step process of solving a linear equation, $5c + 16.5 = 13.5 + 10c$. In this article, we will address some common questions and concerns related to solving linear equations.

Q: What is a linear equation?

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 of $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants.

Q: How do I know if an equation is linear?

To determine if an equation is linear, look for the following characteristics:

• The highest power of the variable(s) is 1.
• The equation can be written in the form of $ax + b = cx + d$.
• The equation does not contain any exponents or roots.

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

The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

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

Q: How do I isolate the variable in a linear equation?

To isolate the variable in a linear equation, follow these steps:

1. Simplify the equation by combining like terms.
2. Add or subtract the same value to both sides of the equation to eliminate any constants.
3. Divide both sides of the equation by the coefficient of the variable to solve for the variable.

Q: What is the difference between a linear equation and a quadratic equation?

A linear equation is an equation in which the highest power of the variable(s) is 1, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation can be written in the form of $ax + b = cx + d$, while a quadratic equation can be written in the form of $ax^2 + bx + c = 0$.

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

Yes, you can use a calculator to solve linear equations. However, it's essential to understand the underlying math and be able to solve the equation by hand. This will help you to:

• Verify the accuracy of the calculator's solution.
• Understand the step-by-step process involved in solving the equation.
• Apply the skills and knowledge to more complex equations.

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

Some common mistakes to avoid when solving linear equations include:

• Not following the order of operations (PEMDAS).
• Not isolating the variable on one side of the equation.
• Not simplifying the equation by combining like terms.
• Not checking the solution for accuracy.

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By understanding the basics of linear equations, following the order of operations (PEMDAS), and avoiding common mistakes, you can become proficient in solving linear equations. Remember to practice solving linear equations to reinforce your understanding and build your confidence.