Solve The Equation:$\[ 2x - 3 + 4x = 21 \\]A. \[$ X = -12 \$\] B. \[$ X = -6 \$\] C. \[$ X = 4 \$\] D. \[$ X = 6 \$\]
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear equation, 2x - 3 + 4x = 21, and provide a step-by-step guide on how to arrive at the correct solution.
Understanding the Equation
The given equation is a linear equation in one variable, x. It is a simple equation that can be solved using basic algebraic operations. The equation is:
2x - 3 + 4x = 21
Step 1: Combine Like Terms
The first step in solving the equation is to combine like terms. In this case, we have two terms with the variable x, which are 2x and 4x. We can combine these terms by adding their coefficients.
2x + 4x = 6x
So, the equation becomes:
6x - 3 = 21
Step 2: Add 3 to Both Sides
The next step is to isolate the variable x by getting rid of the constant term on the left-hand side of the equation. We can do this by adding 3 to both sides of the equation.
6x - 3 + 3 = 21 + 3
This simplifies to:
6x = 24
Step 3: Divide Both Sides by 6
Now that we have isolated the variable x, we can solve for its value by dividing both sides of the equation by 6.
6x / 6 = 24 / 6
This simplifies to:
x = 4
Conclusion
Therefore, the solution to the equation 2x - 3 + 4x = 21 is x = 4. This is the correct answer among the options provided.
Why is this the Correct Answer?
To understand why x = 4 is the correct answer, let's substitute this value back into the original equation and verify that it satisfies the equation.
2(4) - 3 + 4(4) = 8 - 3 + 16
This simplifies to:
21 = 21
As we can see, the equation holds true when x = 4, which confirms that this is the correct solution.
Tips and Tricks
Here are some tips and tricks to help you solve linear equations like this one:
- Always combine like terms first.
- Isolate the variable by getting rid of the constant term on the left-hand side of the equation.
- Use inverse operations to solve for the variable.
- Verify your solution by substituting it back into the original equation.
Common Mistakes to Avoid
Here are some common mistakes to avoid when solving linear equations:
- Not combining like terms.
- Not isolating the variable.
- Not using inverse operations to solve for the variable.
- Not verifying the solution.
Conclusion
Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations like 2x - 3 + 4x = 21 and arrive at the correct solution. Remember to combine like terms, isolate the variable, and use inverse operations to solve for the variable. Verify your solution by substituting it back into the original equation. With practice and patience, you can become proficient in solving linear equations and tackle more complex mathematical problems with confidence.
Final Answer
Introduction
In our previous article, we provided a step-by-step guide on how to solve a linear equation, 2x - 3 + 4x = 21. 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(s) is 1. In other words, it is an equation that can be written in the form ax + b = c, where a, b, and c are constants.
Q: What are the steps to solve a linear equation?
A: The steps to solve a linear equation are:
- Combine like terms.
- Isolate the variable by getting rid of the constant term on the left-hand side of the equation.
- Use inverse operations to solve for the variable.
- Verify the solution by substituting it back into the original equation.
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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, 2x - 3 + 4x = 21 is a linear equation, while x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I know if an equation is linear or quadratic?
A: To determine if an equation is linear or quadratic, look at the highest power of the variable(s). If it is 1, the equation is linear. If it is 2, the equation is quadratic.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not combining like terms.
- Not isolating the variable.
- Not using inverse operations to solve for the variable.
- Not verifying the solution.
Q: How do I verify my solution?
A: To verify your solution, substitute it back into the original equation and check if it satisfies the equation. If it does, then your solution is correct.
Q: What are some tips and tricks for solving linear equations?
A: Some tips and tricks for solving linear equations include:
- Always combine like terms first.
- Isolate the variable by getting rid of the constant term on the left-hand side of the equation.
- Use inverse operations to solve for the variable.
- Verify your solution by substituting it back into the original equation.
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 verify your solution by substituting it back into the original equation.
Conclusion
Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and avoiding common mistakes, you can solve linear equations with confidence. Remember to combine like terms, isolate the variable, and use inverse operations to solve for the variable. Verify your solution by substituting it back into the original equation. With practice and patience, you can become proficient in solving linear equations and tackle more complex mathematical problems with ease.
Final Answer
The final answer is x = 4.