Solve For \[$ X \$\].$\[ 2 = \frac{x+2}{5} \\]

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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 type of linear equation, which is a simple equation with one variable. We will use the given equation 2 = (x+2)/5 as an example to demonstrate the step-by-step process of solving for x.

Understanding the Equation

Before we dive into solving the equation, let's take a closer look at what it means. The equation 2 = (x+2)/5 is a linear equation because it has only one variable, x, and it is set equal to a constant value, 2. The equation is also a simple equation because it does not involve any complex operations or functions.

Step 1: Multiply Both Sides by 5

To solve for x, we need to isolate the variable x on one side of the equation. The first step is to multiply both sides of the equation by 5, which is the denominator of the fraction on the right-hand side. This will eliminate the fraction and make it easier to work with.

2 = (x+2)/5
2 × 5 = (x+2) × 5
10 = x + 2

Step 2: Subtract 2 from Both Sides

Now that we have eliminated the fraction, we can focus on isolating the variable x. The next step is to subtract 2 from both sides of the equation, which will move the constant term to the right-hand side.

10 = x + 2
10 - 2 = x + 2 - 2
8 = x

Step 3: Write the Final Answer

We have now solved for x, and the final answer is x = 8. This means that the value of x that satisfies the equation 2 = (x+2)/5 is 8.

Conclusion

Solving linear equations is an essential skill for students to master, and it requires a step-by-step approach. By following the steps outlined in this article, we can solve for x in the equation 2 = (x+2)/5. Remember to multiply both sides by 5, subtract 2 from both sides, and write the final answer to isolate the variable x.

Tips and Tricks

  • Always start by simplifying the equation and eliminating any fractions or decimals.
  • Use inverse operations to isolate the variable x.
  • Check your work by plugging the final answer back into the original equation.

Real-World Applications

Solving linear equations has many real-world applications, including:

  • Finance: Solving linear equations can help us calculate interest rates, investment returns, and other financial metrics.
  • Science: Solving linear equations can help us model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Solving linear equations can help us design and optimize systems, such as bridges, buildings, and electronic circuits.

Common Mistakes

  • Not simplifying the equation: Failing to simplify the equation can make it difficult to solve for x.
  • Not using inverse operations: Failing to use inverse operations can make it difficult to isolate the variable x.
  • Not checking the work: Failing to check the work can lead to incorrect solutions.

Conclusion

Introduction

In our previous article, we discussed the step-by-step process of solving linear equations. In this article, we will answer some common questions that students often have when it comes to solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation that has only one variable, and it is set equal to a constant value. It can be written in the form ax + b = c, where a, b, and c are constants.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

  • The equation has only one variable.
  • The equation is set equal to a constant value.
  • The equation can be written in the form ax + b = c.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation has only one variable and is set equal to a constant value, while a quadratic equation has two variables and is set equal to a constant value. A quadratic equation can be written in the form ax^2 + bx + c = 0.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow these steps:

  1. Multiply both sides of the equation by the denominator of the fraction.
  2. Simplify the equation.
  3. Use inverse operations to isolate the variable.

Q: What is the inverse operation of addition?

A: The inverse operation of addition is subtraction. For example, if you have the equation x + 2 = 5, the inverse operation would be to subtract 2 from both sides of the equation.

Q: What is the inverse operation of multiplication?

A: The inverse operation of multiplication is division. For example, if you have the equation 2x = 10, the inverse operation would be to divide both sides of the equation by 2.

Q: How do I check my work when solving a linear equation?

A: To check your work, plug the final answer back into the original equation and make sure it is true. For example, if you have the equation x + 2 = 5 and you solve for x, plug the final answer back into the equation to make sure it is true.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not simplifying the equation.
  • Not using inverse operations.
  • Not checking the work.

Q: Can you give me an example of a linear equation with a variable on both sides?

A: Yes, here is an example of a linear equation with a variable on both sides:

x + 2 = 3x - 1

To solve for x, follow these steps:

  1. Add 1 to both sides of the equation.
  2. Subtract 2 from both sides of the equation.
  3. Use inverse operations to isolate the variable.

Conclusion

Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, we can answer some common questions that students often have when it comes to solving linear equations. Remember to simplify the equation, use inverse operations, and check your work to ensure that you are solving the equation correctly.

Tips and Tricks

  • Always start by simplifying the equation and eliminating any fractions or decimals.
  • Use inverse operations to isolate the variable.
  • Check your work by plugging the final answer back into the original equation.

Real-World Applications

Solving linear equations has many real-world applications, including:

  • Finance: Solving linear equations can help us calculate interest rates, investment returns, and other financial metrics.
  • Science: Solving linear equations can help us model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Solving linear equations can help us design and optimize systems, such as bridges, buildings, and electronic circuits.

Common Mistakes

  • Not simplifying the equation: Failing to simplify the equation can make it difficult to solve for x.
  • Not using inverse operations: Failing to use inverse operations can make it difficult to isolate the variable x.
  • Not checking the work: Failing to check the work can lead to incorrect solutions.