2x - 3(7- 2x ) = 5x Solve For X
Introduction
Linear equations are a fundamental concept in algebra, 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(7- 2x ) = 5x, and provide a step-by-step guide on how to solve for x.
Understanding the Equation
Before we dive into solving the equation, let's break it down and understand what it means. The equation is a linear equation, which means it is an equation in which the highest power of the variable (in this case, x) is 1. The equation is also a quadratic equation, which means it can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Step 1: Distribute the Negative Sign
The first step in solving the equation is to distribute the negative sign to the terms inside the parentheses. This will give us:
2x - 3(7- 2x ) = 5x
Distributing the negative sign, we get:
2x - 21 + 6x = 5x
Step 2: Combine Like Terms
The next step is to combine like terms. Like terms are terms that have the same variable and exponent. In this case, we have two like terms: 2x and 6x. We can combine these terms by adding their coefficients:
2x + 6x = 8x
So, the equation becomes:
8x - 21 = 5x
Step 3: Add 21 to Both Sides
The next step is to add 21 to both sides of the equation. This will help us isolate the variable x:
8x - 21 + 21 = 5x + 21
This simplifies to:
8x = 5x + 21
Step 4: Subtract 5x from Both Sides
The next step is to subtract 5x from both sides of the equation. This will help us isolate the variable x:
8x - 5x = 5x + 21 - 5x
This simplifies to:
3x = 21
Step 5: Divide Both Sides by 3
The final step is to divide both sides of the equation by 3. This will give us the value of x:
3x / 3 = 21 / 3
This simplifies to:
x = 7
Conclusion
In this article, we solved the linear equation 2x - 3(7- 2x ) = 5x and found the value of x to be 7. We followed a step-by-step guide to solve the equation, including distributing the negative sign, combining like terms, adding 21 to both sides, subtracting 5x from both sides, and dividing both sides by 3. We hope this article has provided a clear and concise guide on how to solve linear equations.
Tips and Tricks
- When solving linear equations, it's essential to follow the order of operations (PEMDAS) to ensure that you are performing the operations in the correct order.
- When combining like terms, make sure to add or subtract the coefficients of the like terms.
- When adding or subtracting a constant to both sides of the equation, make sure to add or subtract the same constant to both sides.
- When dividing both sides of the equation by a constant, make sure to divide both sides by the same constant.
Common Mistakes
- Failing to distribute the negative sign to the terms inside the parentheses.
- Failing to combine like terms.
- Failing to add or subtract the same constant to both sides of the equation.
- Failing to divide both sides of the equation by the same constant.
Real-World Applications
Linear equations have many real-world applications, including:
- Physics: Linear equations are used to describe the motion of objects under constant acceleration.
- Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
- Economics: Linear equations are used to model economic systems and make predictions about future economic trends.
Conclusion
Introduction
In our previous article, we solved the linear equation 2x - 3(7- 2x ) = 5x and found the value of x to be 7. However, we know that there are many more linear equations out there, and each one requires a unique solution. In this article, we will provide a Q&A guide to help you solve linear equations like a pro.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable (in this case, x) is 1. It 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 follow these steps:
- Distribute the negative sign to the terms inside the parentheses.
- Combine like terms.
- Add or subtract the same constant to both sides of the equation.
- Divide both sides of the equation by the same constant.
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:
- 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 distribute the negative sign?
A: To distribute the negative sign, you need to multiply the negative sign by each term inside the parentheses. For example, if you have the equation -2(x + 3), you would distribute the negative sign as follows:
-2(x + 3) = -2x - 6
Q: What are like terms?
A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms because they both have the variable x and the exponent 1.
Q: How do I combine like terms?
A: To combine like terms, you need to add or subtract the coefficients of the like terms. For example, if you have the equation 2x + 4x, you would combine the like terms as follows:
2x + 4x = 6x
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 (in this case, x) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable (in this case, x) is 2. For example, the equation x^2 + 4x + 4 is a quadratic equation because it has a highest power of 2.
Q: How do I solve a quadratic equation?
A: To solve a quadratic equation, you need to follow these steps:
- Factor the quadratic expression, if possible.
- Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
- Simplify the expression and solve for x.
Q: What is the quadratic formula?
A: The quadratic formula is a formula that allows you to solve quadratic equations. It is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Q: How do I use the quadratic formula?
A: To use the quadratic formula, you need to plug in the values of a, b, and c into the formula. For example, if you have the equation x^2 + 4x + 4 = 0, you would plug in the values a = 1, b = 4, and c = 4 into the formula.
Conclusion
In this article, we provided a Q&A guide to help you solve linear equations like a pro. We covered topics such as the order of operations, distributing the negative sign, combining like terms, and solving quadratic equations. We hope this article has provided you with a clear and concise guide on how to solve linear equations.
Tips and Tricks
- Make sure to follow the order of operations (PEMDAS) when solving equations.
- Distribute the negative sign to the terms inside the parentheses.
- Combine like terms by adding or subtracting the coefficients.
- Use the quadratic formula to solve quadratic equations.
Common Mistakes
- Failing to distribute the negative sign to the terms inside the parentheses.
- Failing to combine like terms.
- Failing to use the quadratic formula to solve quadratic equations.
Real-World Applications
Linear equations have many real-world applications, including:
- Physics: Linear equations are used to describe the motion of objects under constant acceleration.
- Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
- Economics: Linear equations are used to model economic systems and make predictions about future economic trends.
Conclusion
In conclusion, solving linear equations is a crucial skill for students to master. By following a step-by-step guide and understanding the concepts of linear equations, students can solve equations like 2x - 3(7- 2x ) = 5x and find the value of x. We hope this article has provided a clear and concise guide on how to solve linear equations.