3x+7=2x-4+5x Find The Value Of X
Introduction
In mathematics, solving linear equations is a fundamental concept that helps us understand the relationship between variables. In this article, we will focus on solving a linear equation of the form 3x+7=2x-4+5x, where we need to find the value of x. This equation involves basic algebraic operations, and by following a step-by-step approach, we can easily solve for x.
Understanding the Equation
The given equation is 3x+7=2x-4+5x. To solve for x, we need to isolate the variable x on one side of the equation. The equation involves addition, subtraction, multiplication, and division operations, which we will use to simplify the equation and find the value of x.
Step 1: Simplify the Right-Hand Side of the Equation
The first step is to simplify the right-hand side of the equation by combining like terms. The right-hand side of the equation is 2x-4+5x. We can combine the like terms 2x and 5x by adding them together, which gives us 7x-4.
2x - 4 + 5x = 7x - 4
Step 2: Rewrite the Equation with the Simplified Right-Hand Side
Now that we have simplified the right-hand side of the equation, we can rewrite the original equation as 3x+7=7x-4.
3x + 7 = 7x - 4
Step 3: Add 4 to Both Sides of the Equation
To isolate the variable x, we need to get rid of the constant term -4 on the right-hand side of the equation. We can do this by adding 4 to both sides of the equation. This gives us 3x+7+4=7x.
3x + 7 + 4 = 7x
Step 4: Simplify the Left-Hand Side of the Equation
Now that we have added 4 to both sides of the equation, we can simplify the left-hand side by combining the like terms 7 and 4. This gives us 3x+11=7x.
3x + 11 = 7x
Step 5: Subtract 3x from Both Sides of the Equation
To isolate the variable x, we need to get rid of the term 3x on the left-hand side of the equation. We can do this by subtracting 3x from both sides of the equation. This gives us 11=4x.
11 = 4x
Step 6: Divide Both Sides of the Equation by 4
Finally, to find the value of x, we need to isolate x by dividing both sides of the equation by 4. This gives us x=11/4.
x = 11/4
Conclusion
In this article, we have solved the linear equation 3x+7=2x-4+5x to find the value of x. By following a step-by-step approach, we have simplified the equation, isolated the variable x, and found the value of x to be 11/4. This equation involves basic algebraic operations, and by understanding the concept of linear equations, we can easily solve for x.
Frequently Asked Questions
- What is the value of x in the equation 3x+7=2x-4+5x?
- How do we simplify the right-hand side of the equation?
- What is the step-by-step approach to solving the linear equation?
Final Answer
The final answer is x=11/4.
Introduction
In our previous article, we solved the linear equation 3x+7=2x-4+5x to find the value of x. In this article, we will provide a Q&A guide to help you understand the concept of linear equations and how to solve them. Whether you are a student or a teacher, this guide will help you to clarify any doubts you may have about solving linear equations.
Q&A Guide
Q1: What is a linear equation?
A1: A linear equation is an equation in which the highest power of the variable (x) is 1. It is a simple equation that can be solved using basic algebraic operations.
Q2: How do I simplify the right-hand side of the equation?
A2: To simplify the right-hand side of the equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, in the equation 2x-4+5x, you can combine the like terms 2x and 5x by adding them together, which gives you 7x-4.
Q3: What is the step-by-step approach to solving the linear equation?
A3: The step-by-step approach to solving the linear equation is as follows:
- Simplify the right-hand side of the equation by combining like terms.
- Rewrite the equation with the simplified right-hand side.
- Add or subtract the same value to both sides of the equation to isolate the variable x.
- Simplify the left-hand side of the equation by combining like terms.
- Divide both sides of the equation by the coefficient of x to find the value of x.
Q4: How do I isolate the variable x?
A4: To isolate the variable x, you need to get rid of the constant term on the right-hand side of the equation. You can do this by adding or subtracting the same value to both sides of the equation.
Q5: What is the final answer to the equation 3x+7=2x-4+5x?
A5: The final answer to the equation 3x+7=2x-4+5x is x=11/4.
Q6: Can I use the same steps to solve other linear equations?
A6: Yes, you can use the same steps to solve other linear equations. The steps are general and can be applied to any linear equation.
Q7: What if I have a linear equation with fractions?
A7: If you have a linear equation with fractions, you can simplify the equation by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.
Q8: Can I use a calculator to solve linear equations?
A8: Yes, you can use a calculator to solve linear equations. However, it is always a good idea to check your answer by plugging it back into the original equation.
Conclusion
In this Q&A guide, we have provided answers to some of the most common questions about solving linear equations. Whether you are a student or a teacher, this guide will help you to clarify any doubts you may have about solving linear equations. Remember to always follow the step-by-step approach and to simplify the equation by combining like terms.
Frequently Asked Questions
- What is a linear equation?
- How do I simplify the right-hand side of the equation?
- What is the step-by-step approach to solving the linear equation?
- How do I isolate the variable x?
- What is the final answer to the equation 3x+7=2x-4+5x?
Final Answer
The final answer is x=11/4.