Solve The Equation:$\[ 2(2-x) = X-2 \\]
Introduction
In mathematics, equations are a fundamental concept that help us understand and describe various relationships between variables. Solving equations is a crucial skill that is essential in many areas of mathematics, science, and engineering. In this article, we will focus on solving a specific equation: 2(2-x) = x-2. We will break down the solution step by step, using algebraic manipulations to isolate the variable x.
Understanding the Equation
The given equation is 2(2-x) = x-2. To solve this equation, we need to isolate the variable x. The first step is to simplify the left-hand side of the equation by distributing the 2 to the terms inside the parentheses.
Distributing the 2
When we distribute the 2 to the terms inside the parentheses, we get:
2(2-x) = 2(2) - 2(x)
Using the distributive property, we can simplify this expression to:
4 - 2x = x - 2
Simplifying the Equation
Now that we have simplified the left-hand side of the equation, we can combine like terms to get:
4 - 2x = x - 2
To get rid of the negative term on the left-hand side, we can add 2x to both sides of the equation. This gives us:
4 = 3x - 2
Isolating the Variable x
Now that we have isolated the variable x, we can solve for x by adding 2 to both sides of the equation. This gives us:
6 = 3x
To solve for x, we can divide both sides of the equation by 3. This gives us:
x = 2
Checking the Solution
To check our solution, we can plug x = 2 back into the original equation. If the equation holds true, then our solution is correct.
2(2-2) = 2-2
Using the distributive property, we can simplify the left-hand side of the equation to:
2(0) = 0
This simplifies to:
0 = 0
Since the equation holds true, our solution x = 2 is correct.
Conclusion
In this article, we solved the equation 2(2-x) = x-2 by simplifying the left-hand side of the equation, combining like terms, and isolating the variable x. We then checked our solution by plugging x = 2 back into the original equation. Our solution x = 2 is correct, and we have successfully solved the equation.
Frequently Asked Questions
- Q: What is the first step in solving the equation 2(2-x) = x-2? A: The first step is to simplify the left-hand side of the equation by distributing the 2 to the terms inside the parentheses.
- Q: How do we get rid of the negative term on the left-hand side of the equation? A: We can add 2x to both sides of the equation to get rid of the negative term.
- Q: How do we check our solution? A: We can plug x = 2 back into the original equation to check if it holds true.
Final Answer
The final answer is x = 2.
Introduction
In our previous article, we solved the equation 2(2-x) = x-2 by simplifying the left-hand side of the equation, combining like terms, and isolating the variable x. In this article, we will provide a Q&A section to help clarify any doubts or questions that readers may have.
Q&A
Q: What is the first step in solving the equation 2(2-x) = x-2?
A: The first step is to simplify the left-hand side of the equation by distributing the 2 to the terms inside the parentheses. This will help us to get rid of the parentheses and make the equation easier to work with.
Q: How do we get rid of the negative term on the left-hand side of the equation?
A: We can add 2x to both sides of the equation to get rid of the negative term. This will help us to isolate the variable x and make it easier to solve for.
Q: How do we check our solution?
A: We can plug x = 2 back into the original equation to check if it holds true. If the equation holds true, then our solution is correct.
Q: What if the equation has multiple solutions?
A: If the equation has multiple solutions, then we need to find all of the possible values of x that satisfy the equation. We can do this by using algebraic manipulations and solving for x.
Q: How do we know if the equation has a solution?
A: We can use the concept of a "solution set" to determine if the equation has a solution. If the solution set is empty, then the equation has no solution. If the solution set is non-empty, then the equation has at least one solution.
Q: Can we use the same method to solve other types of equations?
A: Yes, we can use the same method to solve other types of equations, such as linear equations, quadratic equations, and polynomial equations. However, we may need to use different algebraic manipulations and techniques to solve these types of equations.
Q: What if the equation has a variable on both sides?
A: If the equation has a variable on both sides, then we need to use algebraic manipulations to isolate the variable on one side of the equation. We can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Q: How do we know if the equation is true or false?
A: We can use the concept of a "truth table" to determine if the equation is true or false. A truth table is a table that shows the possible values of the variables and the corresponding truth values of the equation.
Conclusion
In this article, we provided a Q&A section to help clarify any doubts or questions that readers may have about solving the equation 2(2-x) = x-2. We covered topics such as simplifying the left-hand side of the equation, getting rid of the negative term, checking the solution, and using algebraic manipulations to solve for x.
Final Answer
The final answer is x = 2.
Additional Resources
- For more information on solving equations, please see our previous article on solving the equation 2(2-x) = x-2.
- For more information on algebraic manipulations, please see our article on algebraic manipulations.
- For more information on truth tables, please see our article on truth tables.
Related Articles
- Solving the Equation: 2(2-x) = x-2
- Algebraic Manipulations
- Truth Tables
Tags
- Solving equations
- Algebraic manipulations
- Truth tables
- Linear equations
- Quadratic equations
- Polynomial equations
- Variables
- Algebra
- Mathematics