After The Bank Cashed A Check Maureen Wrote For \[$\$60\$\], Her Balance Was \[$-\$14\$\]. The Equation \[$b + (-60) = -14\$\] Can Be Used To Represent This Situation, Where \[$b\$\] Is Maureen's Balance, In Dollars,
Introduction
Linear equations are a fundamental concept in mathematics, and they have numerous applications in various fields, including finance, science, and engineering. In this article, we will explore a real-world example of a linear equation and demonstrate how to solve it. We will use the scenario of Maureen's bank account to illustrate the concept of linear equations and provide a step-by-step solution.
The Problem
Maureen wrote a check for $60, and after the bank cashed it, her balance was -$14. We can represent this situation using the equation b + (-60) = -14, where b is Maureen's balance in dollars.
Understanding the Equation
The equation b + (-60) = -14 is a linear equation, which means it is an equation in which the highest power of the variable (in this case, b) is 1. The equation is in the form of ax + b = c, where a, b, and c are constants. In this case, a = 1, b = -60, and c = -14.
Solving the Equation
To solve the equation b + (-60) = -14, we need to isolate the variable b. We can do this by adding 60 to both sides of the equation, which will eliminate the negative term.
b + (-60) = -14
b + (-60) + 60 = -14 + 60
b = 46
Interpreting the Solution
The solution to the equation b + (-60) = -14 is b = 46. This means that Maureen's balance in her bank account is $46.
Real-World Applications
Linear equations have numerous real-world applications, including finance, science, and engineering. In finance, linear equations are used to calculate interest rates, investment returns, and loan payments. In science, linear equations are used to model population growth, chemical reactions, and physical systems. In engineering, linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Conclusion
In conclusion, linear equations are a fundamental concept in mathematics, and they have numerous applications in various fields. The scenario of Maureen's bank account provides a real-world example of a linear equation and demonstrates how to solve it. By understanding and solving linear equations, we can make informed decisions and solve problems in a variety of contexts.
Additional Examples
Here are a few additional examples of linear equations:
- 2x + 5 = 11
- x - 3 = 7
- 4y - 2 = 10
Solving Linear Equations: Tips and Tricks
Here are a few tips and tricks for solving linear equations:
- Always isolate the variable on one side of the equation.
- Use inverse operations to eliminate the variable.
- Check your solution by plugging it back into the original equation.
Common Mistakes to Avoid
Here are a few common mistakes to avoid when solving linear equations:
- Not isolating the variable on one side of the equation.
- Not using inverse operations to eliminate the variable.
- Not checking your solution by plugging it back into the original equation.
Conclusion
Introduction
In our previous article, we explored a real-world example of a linear equation and demonstrated how to solve it. In this article, we will answer some frequently asked questions 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 is 1. It is an equation in which the variable is not raised to a power greater than 1.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division.
Q: What is an inverse operation?
A: An inverse operation is an operation that undoes another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
Q: How do I use inverse operations to solve a linear equation?
A: To use inverse operations to solve a linear equation, you need to identify the operation that is being performed on the variable. Then, you need to perform the inverse operation to isolate the variable.
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:
- 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 check my solution?
A: To check your solution, you need to plug it back into the original equation and see if it is true. If the solution is true, then you have found the correct solution.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not isolating the variable on one side of the equation.
- Not using inverse operations to eliminate the variable.
- Not checking your solution by plugging it back into the original equation.
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 of the denominators.
Q: How do I solve a linear equation with decimals?
A: To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10.
Q: Can I use a calculator to solve linear equations?
A: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check your solution by plugging it back into the original equation.
Conclusion
In conclusion, solving linear equations is a fundamental skill in mathematics, and it has numerous applications in various fields. By understanding and solving linear equations, we can make informed decisions and solve problems in a variety of contexts.