What Is The Value Of $x$ In The Equation $1.5(x+4)-3=4.5(x-2)$?A. 3 B. 4 C. 5 D. 9

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Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics, and it is essential to understand how to manipulate and solve these equations to find the value of unknown variables. In this article, we will focus on solving a specific linear equation, $1.5(x+4)-3=4.5(x-2)$, to find the value of $x$. We will break down the steps involved in solving this equation and provide a clear explanation of each step.

Understanding the Equation

The given 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:

1.5(x+4)−3=4.5(x−2)1.5(x+4)-3=4.5(x-2)

To solve this equation, we need to isolate the variable $x$ on one side of the equation. We can start by simplifying the equation by distributing the coefficients to the terms inside the parentheses.

Distributing Coefficients

To distribute the coefficients, we multiply each term inside the parentheses by the coefficient outside the parentheses. In this case, we have:

1.5(x+4)−3=4.5(x−2)1.5(x+4)-3=4.5(x-2)

Distributing the coefficients, we get:

1.5x+6−3=4.5x−91.5x+6-3=4.5x-9

Combining Like Terms

Now that we have distributed the coefficients, we can combine like terms on each side of the equation. Like terms are terms that have the same variable raised to the same power. In this case, we have:

1.5x+6−3=4.5x−91.5x+6-3=4.5x-9

Combining like terms, we get:

1.5x+3=4.5x−91.5x+3=4.5x-9

Isolating the Variable

To isolate the variable $x$, we need to get all the terms with $x$ on one side of the equation and the constant terms on the other side. We can do this by subtracting $1.5x$ from both sides of the equation.

1.5x+3−1.5x=4.5x−9−1.5x1.5x+3-1.5x=4.5x-9-1.5x

Simplifying the equation, we get:

3=2.5x−93=2.5x-9

Adding Constants

To isolate the variable $x$, we need to get all the constant terms on one side of the equation. We can do this by adding 9 to both sides of the equation.

3+9=2.5x−9+93+9=2.5x-9+9

Simplifying the equation, we get:

12=2.5x12=2.5x

Dividing by Coefficients

To find the value of $x$, we need to divide both sides of the equation by the coefficient of $x$. In this case, the coefficient of $x$ is 2.5.

122.5=2.5x2.5\frac{12}{2.5}=\frac{2.5x}{2.5}

Simplifying the equation, we get:

4.8=x4.8=x

Conclusion

In this article, we solved a linear equation, $1.5(x+4)-3=4.5(x-2)$, to find the value of $x$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. We distributed coefficients, combined like terms, isolated the variable, added constants, and divided by coefficients to find the value of $x$. The final answer is $x=4.8$.

Discussion

The value of $x$ in the equation $1.5(x+4)-3=4.5(x-2)$ is $x=4.8$. This is the solution to the equation, and it can be verified by plugging the value of $x$ back into the original equation.

Final Answer

The final answer is: 4.8\boxed{4.8}

Introduction

In our previous article, we solved a linear equation, $1.5(x+4)-3=4.5(x-2)$, to find the value of $x$. We broke down the steps involved in solving this equation and provided a clear explanation of each step. 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 (in this case, $x$) is 1. It is a simple equation that can be solved by using basic algebraic operations.

Q: How do I solve a linear equation?

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

Q: What are the steps involved in solving a linear equation?

A: The steps involved in solving a linear equation are:

  1. Distribute coefficients to the terms inside the parentheses.
  2. Combine like terms on each side of the equation.
  3. Isolate the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side.
  4. Add or subtract constants to isolate the variable.
  5. Divide by coefficients to find the value of the variable.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. Quadratic equations are more complex and require more advanced algebraic operations to solve.

Q: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation. However, it is always a good idea to check your work by plugging the value of the variable back into the original equation.

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

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

  • Not distributing coefficients to the terms inside the parentheses.
  • Not combining like terms on each side of the equation.
  • Not isolating the variable by getting all the terms with the variable on one side of the equation and the constant terms on the other side.
  • Not adding or subtracting constants to isolate the variable.
  • Not dividing by coefficients to find the value of the variable.

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

A: To check your work, plug the value of the variable back into the original equation and simplify. If the equation is true, then your solution is correct.

Q: What are some real-world applications of linear equations?

A: 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 bridges, buildings, and electronic circuits.
  • Economics: Linear equations are used to model economic systems and make predictions about future economic trends.
  • Computer Science: Linear equations are used in computer graphics and game development to create realistic simulations.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. We covered topics such as the definition of a linear equation, the steps involved in solving a linear equation, and common mistakes to avoid. We also discussed real-world applications of linear equations and how to check your work when solving a linear equation.

Final Answer

The final answer is: 4.8\boxed{4.8}