Solve $2x - 1 = 5$.A. $x = 1$ B. $ X = 2 X = 2 X = 2 [/tex] C. $x = 3$ D. $x = 4$

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Introduction

In this article, we will focus on solving a linear equation of the form 2x - 1 = 5. This type of equation is a fundamental concept in algebra and is essential for solving various mathematical problems. We will use the correct method to solve this equation and provide the solution in the required format.

Understanding the Equation

The given equation is 2x - 1 = 5. To solve for x, we need to isolate the variable x on one side of the equation. The equation is a linear equation, which means it can be written in the form ax + b = c, where a, b, and c are constants.

Step 1: Add 1 to Both Sides of the Equation

To isolate the term with x, we need to get rid of the constant term -1 on the left side of the equation. We can do this by adding 1 to both sides of the equation. This will give us:

2x - 1 + 1 = 5 + 1

Step 2: Simplify the Equation

After adding 1 to both sides of the equation, we get:

2x = 6

Step 3: Divide Both Sides by 2

To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 2. This will give us:

(2x) / 2 = 6 / 2

Step 4: Simplify the Equation

After dividing both sides of the equation by 2, we get:

x = 3

Conclusion

Therefore, the solution to the linear equation 2x - 1 = 5 is x = 3. This means that the value of x that satisfies the equation is 3.

Answer Options

Based on the solution we obtained, we can see that the correct answer is:

C. x = 3

Discussion

The equation 2x - 1 = 5 is a simple linear equation that can be solved using basic algebraic operations. The solution involves adding 1 to both sides of the equation, simplifying the equation, and then dividing both sides by 2. This type of equation is essential for solving various mathematical problems, and understanding how to solve it is crucial for success in mathematics.

Tips and Tricks

  • When solving linear equations, it's essential to isolate the variable x on one side of the equation.
  • Use basic algebraic operations such as addition, subtraction, multiplication, and division to simplify the equation.
  • Make sure to check your solution by plugging it back into the original equation.

Related Topics

  • Solving quadratic equations
  • Solving systems of linear equations
  • Graphing linear equations

Final Answer

The final answer is C. x = 3.

Introduction

In our previous article, we solved the linear equation 2x - 1 = 5 and obtained the solution x = 3. In this article, we will provide a Q&A section to help you understand the concept of solving linear equations better.

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 can be written in the form ax + b = c, where a, b, and c are constants.

Q2: How do I solve a linear equation?

A2: To solve a linear equation, you need to isolate the variable x on one side of the equation. You can do this by using basic algebraic operations such as addition, subtraction, multiplication, and division.

Q3: What is the first step in solving a linear equation?

A3: The first step in solving a linear equation is to get rid of any constants on the same side of the equation as the variable x. You can do this by adding or subtracting the same value to both sides of the equation.

Q4: How do I simplify an equation?

A4: To simplify an equation, you need to combine like terms and eliminate any unnecessary operations. For example, if you have the equation 2x + 3x = 5, you can combine the like terms 2x and 3x to get 5x = 5.

Q5: What is the difference between a linear equation and a quadratic equation?

A5: A linear equation is an equation in which the highest power of the variable (x) is 1, while a quadratic equation is an equation in which the highest power of the variable (x) is 2. For example, the equation 2x - 1 = 5 is a linear equation, while the equation x^2 + 2x + 1 = 0 is a quadratic equation.

Q6: How do I check my solution?

A6: To check your solution, you need to plug it back into the original equation and see if it is true. For example, if you solve the equation 2x - 1 = 5 and get x = 3, you can plug x = 3 back into the equation to see if it is true: 2(3) - 1 = 5, which simplifies to 6 - 1 = 5, and is indeed true.

Q7: What are some common mistakes to avoid when solving linear equations?

A7: Some common mistakes to avoid when solving linear equations include:

  • Not isolating the variable x on one side of the equation
  • Not combining like terms
  • Not checking your solution
  • Not using the correct order of operations

Q8: How do I graph a linear equation?

A8: To graph a linear equation, you need to find two points on the line and plot them on a coordinate plane. You can then draw a line through the two points to represent the equation.

Q9: What is the significance of linear equations in real-life applications?

A9: Linear equations have many real-life applications, including:

  • Modeling population growth
  • Calculating interest rates
  • Determining the cost of goods
  • Solving problems in physics and engineering

Q10: How can I practice solving linear equations?

A10: You can practice solving linear equations by working through example problems, using online resources, and taking practice quizzes. You can also try solving linear equations in your everyday life, such as calculating the cost of groceries or determining the time it takes to complete a task.

Conclusion

Solving linear equations is an essential skill in mathematics and has many real-life applications. By understanding the concept of linear equations and practicing solving them, you can become proficient in solving a wide range of mathematical problems.