Solve The Equation: ${ -6 + \frac{x}{4} = -5 }$
Introduction
Solving linear equations is a fundamental concept in mathematics that involves isolating the variable on one side of the equation. In this article, we will focus on solving the equation -6 + x/4 = -5, which is a simple linear equation. We will break down the solution into step-by-step instructions, making it easy to understand and follow.
Understanding the Equation
The given equation is -6 + x/4 = -5. This equation involves a fraction, which can be solved using basic algebraic operations. The goal is to isolate the variable x on one side of the equation.
Step 1: Add 6 to Both Sides of the Equation
To start solving the equation, we need to get rid of the constant term -6 on the left side of the equation. We can do this by adding 6 to both sides of the equation. This will keep the equation balanced and ensure that we are not changing the value of the equation.
-6 + x/4 = -5
Adding 6 to both sides:
-6 + 6 + x/4 = -5 + 6
x/4 = 1
Step 2: Multiply Both Sides of the Equation by 4
Now that we have isolated the fraction x/4 on the left side of the equation, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 4. This will eliminate the fraction and give us the value of x.
x/4 = 1
Multiplying both sides by 4:
x/4 * 4 = 1 * 4
x = 4
Conclusion
In this article, we solved the linear equation -6 + x/4 = -5 using basic algebraic operations. We added 6 to both sides of the equation to isolate the fraction x/4, and then multiplied both sides of the equation by 4 to eliminate the fraction and find the value of x. The final solution is x = 4.
Tips and Tricks
- When solving linear equations, it's essential to keep the equation balanced by performing the same operation on both sides of the equation.
- To eliminate fractions, multiply both sides of the equation by the denominator of the fraction.
- To add or subtract fractions, find a common denominator and then perform the operation.
Real-World Applications
Solving linear equations has numerous real-world applications in various fields, including:
- Physics: Solving linear equations is essential in physics to describe the motion of objects and calculate their velocities and accelerations.
- Engineering: Linear equations are used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
- Economics: Solving linear equations is used in economics to model and analyze economic systems, including supply and demand curves.
Common Mistakes to Avoid
- When solving linear equations, it's easy to make mistakes by not keeping the equation balanced or by not eliminating fractions correctly.
- To avoid these mistakes, make sure to perform the same operation on both sides of the equation and eliminate fractions by multiplying both sides by the denominator.
Final Thoughts
Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By following the step-by-step instructions outlined in this article, you can solve linear equations with ease and confidence. Remember to keep the equation balanced, eliminate fractions correctly, and apply the concepts to real-world problems. With practice and patience, you will become proficient in solving linear equations and be able to tackle more complex equations with ease.
Introduction
In our previous article, we solved the linear equation -6 + x/4 = -5 using basic algebraic operations. In this article, we will answer some frequently asked questions about solving linear equations. Whether you're a student, teacher, or simply someone who wants to improve their math skills, this Q&A guide will provide you with the answers you need to tackle linear equations with confidence.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable (usually x) is 1. In other words, it's an equation that can be written in the form ax + b = c, where a, b, and c are constants.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable (usually x) on one side of the equation. You can do this by performing basic algebraic operations such as addition, subtraction, multiplication, and division.
Q: What is the order of operations when solving linear equations?
A: When solving linear equations, you need to follow the order of operations (PEMDAS):
- 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 eliminate fractions when solving linear equations?
A: To eliminate fractions, multiply both sides of the equation by the denominator of the fraction. This will get rid of the fraction and allow you to solve for the variable.
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. For example, the equation x + 2 = 3 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic 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 underlying math concepts and be able to solve equations by hand. This will help you to check your work and ensure that your calculator is giving you the correct answer.
Q: How do I check my work when solving linear equations?
A: To check your work, plug your solution back into the original equation and make sure that it's true. If your solution is correct, the equation should balance and the two sides should be equal.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not keeping the equation balanced
- Not eliminating fractions correctly
- Not following the order of operations
- Not checking your work
Q: Can I use linear equations to solve real-world problems?
A: Yes, linear equations can be used to solve a wide range of real-world problems, including physics, engineering, economics, and more. By applying the concepts of linear equations to real-world problems, you can develop a deeper understanding of the underlying math and improve your problem-solving skills.
Conclusion
Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By following the step-by-step instructions outlined in this article and answering the frequently asked questions, you can improve your math skills and become proficient in solving linear equations. Remember to keep the equation balanced, eliminate fractions correctly, and apply the concepts to real-world problems. With practice and patience, you will become a master of solving linear equations and be able to tackle more complex equations with ease.