What Is The Solution To The Equation?${ 5 + 4x = 2 }$A. { X = -\frac{4}{3} $}$ B. { X = -\frac{3}{4} $}$ C. { X = \frac{7}{4} $}$ D. { X = -\frac{4}{7} $}$
Introduction
In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. An equation is a statement that expresses the equality of two mathematical expressions. It can be a simple linear equation or a complex equation involving various mathematical operations. In this article, we will focus on solving a simple linear equation and explore the different methods to find the solution.
Understanding the Equation
The given equation is:
5 + 4x = 2
This is a linear equation in one variable, where x is the unknown variable. The equation is in the form of an inequality, where the left-hand side is greater than the right-hand side. To solve for x, we need to isolate the variable on one side of the equation.
Isolating the Variable
To isolate the variable x, we need to get rid of the constant term on the left-hand side. We can do this by subtracting 5 from both sides of the equation.
5 + 4x - 5 = 2 - 5
This simplifies to:
4x = -3
Solving for x
Now that we have isolated the variable x, we can solve for its value. To do this, we need to divide both sides of the equation by 4.
4x / 4 = -3 / 4
This simplifies to:
x = -3/4
Checking the Solution
To verify that our solution is correct, we can plug it back into the original equation.
5 + 4(-3/4) = 2
Simplifying this expression, we get:
5 - 3 = 2
This is a true statement, which confirms that our solution is correct.
Conclusion
In this article, we solved a simple linear equation using the method of isolating the variable. We started with the equation 5 + 4x = 2 and isolated the variable x by subtracting 5 from both sides. We then solved for x by dividing both sides of the equation by 4. Our solution was x = -3/4, which we verified by plugging it back into the original equation.
Comparison with Options
Now that we have solved the equation, let's compare our solution with the options provided.
A. x = -4/3 B. x = -3/4 C. x = 7/4 D. x = -4/7
Our solution, x = -3/4, matches option B. Therefore, the correct answer is:
The correct answer is B. x = -3/4
Final Thoughts
Solving equations is an essential skill in mathematics, and it requires a deep understanding of algebraic operations and techniques. In this article, we demonstrated how to solve a simple linear equation using the method of isolating the variable. We also compared our solution with the options provided and verified that our solution is correct. With practice and patience, anyone can master the art of solving equations and become proficient in mathematics.
Frequently Asked Questions
- Q: What is the solution to the equation 5 + 4x = 2? A: The solution to the equation is x = -3/4.
- Q: How do I isolate the variable in a linear equation? A: To isolate the variable, you need to get rid of the constant term on the left-hand side by subtracting it from both sides of the equation.
- Q: How do I solve for x in a linear equation? A: To solve for x, you need to divide both sides of the equation by the coefficient of x.
Additional Resources
- For more information on solving linear equations, visit the Khan Academy website.
- For practice problems and exercises, visit the Mathway website.
- For a comprehensive guide to algebra, visit the Algebra.com website.
Conclusion
In conclusion, solving equations is a fundamental concept in mathematics that requires a deep understanding of algebraic operations and techniques. In this article, we demonstrated how to solve a simple linear equation using the method of isolating the variable. We also compared our solution with the options provided and verified that our solution is correct. With practice and patience, anyone can master the art of solving equations and become proficient in mathematics.
Introduction
Solving linear equations is a fundamental concept in mathematics that can be a bit challenging for some students. In our previous article, we demonstrated how to solve a simple linear equation using the method of isolating the variable. However, we know that there are many more questions and doubts that students may have when it comes to solving linear equations. In this article, we will address some of the most frequently asked questions about 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 (usually x) is 1. It can be written in the form of 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) by getting rid of the constant term on the left-hand side. You can do this by subtracting the constant term from both sides of the equation.
Q: What is the method of isolating the variable?
A: The method of isolating the variable is a technique used to solve linear equations. It involves getting rid of the constant term on the left-hand side by subtracting it from both sides of the equation.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable, you need to get rid of the constant term on the left-hand side by subtracting it from both sides of the equation. For example, if you have the equation 2x + 3 = 5, you can isolate the variable by subtracting 3 from both sides: 2x = 5 - 3, which simplifies to 2x = 2.
Q: How do I solve for x in a linear equation?
A: To solve for x, you need to divide both sides of the equation by the coefficient of x. For example, if you have the equation 2x = 4, you can solve for x by dividing both sides by 2: x = 4/2, which simplifies to x = 2.
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 (usually x) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable (usually x) is 2. For example, the equation x^2 + 2x + 1 = 0 is a quadratic equation, while the equation 2x + 3 = 5 is a linear equation.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are constants.
Q: What is the quadratic formula?
A: The quadratic formula is a formula used to solve quadratic equations. It is given by: x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are constants.
Q: How do I use the quadratic formula to solve a quadratic equation?
A: To use the quadratic formula, you need to plug in the values of a, b, and c into the formula and simplify. For example, if you have the equation x^2 + 2x + 1 = 0, you can use the quadratic formula to solve for x: x = (-2 ± √(2^2 - 4(1)(1))) / 2(1), which simplifies to x = (-2 ± √(4 - 4)) / 2, which further simplifies to x = (-2 ± √0) / 2, which finally simplifies to x = -2/2, which equals x = -1.
Conclusion
In this article, we addressed some of the most frequently asked questions about solving linear equations. We covered topics such as the method of isolating the variable, solving for x, and the difference between linear and quadratic equations. We also provided examples and explanations to help students understand the concepts better. We hope that this article has been helpful in clarifying any doubts that students may have had about solving linear equations.
Additional Resources
- For more information on solving linear equations, visit the Khan Academy website.
- For practice problems and exercises, visit the Mathway website.
- For a comprehensive guide to algebra, visit the Algebra.com website.
Final Thoughts
Solving linear equations is an essential skill in mathematics that requires a deep understanding of algebraic operations and techniques. In this article, we demonstrated how to solve a simple linear equation using the method of isolating the variable. We also addressed some of the most frequently asked questions about solving linear equations and provided examples and explanations to help students understand the concepts better. With practice and patience, anyone can master the art of solving linear equations and become proficient in mathematics.