Find The Value Of $x$ In The Equation $9 - 4x = 57$.A. 16.5 B. -16.5 C. -12 D. 12

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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 linear equation of the form $ax + b = c$, where $a$, $b$, and $c$ are constants. We will use the equation $9 - 4x = 57$ as an example to demonstrate the step-by-step process of solving linear equations.

Understanding the Equation

Before we start solving the equation, let's take a closer look at it. The equation is $9 - 4x = 57$. We can see that it is a linear equation, where the variable $x$ is multiplied by a constant $-4$ and then added to a constant $9$. The equation is set equal to a constant $57$.

Step 1: Isolate the Variable

The first step in solving a linear equation is to isolate the variable $x$. To do this, we need to get rid of the constant term on the same side of the equation as the variable. In this case, we can add $4x$ to both sides of the equation to get rid of the $-4x$ term.

9−4x+4x=57+4x9 - 4x + 4x = 57 + 4x

This simplifies to:

9=57+4x9 = 57 + 4x

Step 2: Get Rid of the Constant Term

Now that we have isolated the variable $x$, we need to get rid of the constant term on the same side of the equation. In this case, we can subtract $57$ from both sides of the equation to get rid of the $57$ term.

9−57=4x9 - 57 = 4x

This simplifies to:

−48=4x-48 = 4x

Step 3: Solve for the Variable

Now that we have isolated the variable $x$ and gotten rid of the constant term, we can solve for $x$. To do this, we need to divide both sides of the equation by the coefficient of the variable, which is $4$.

−484=4x4\frac{-48}{4} = \frac{4x}{4}

This simplifies to:

−12=x-12 = x

Conclusion

In this article, we have demonstrated the step-by-step process of solving a linear equation of the form $ax + b = c$. We used the equation $9 - 4x = 57$ as an example and showed how to isolate the variable, get rid of the constant term, and solve for the variable. The final answer is $x = -12$.

Answer

The correct answer is:

  • C. -12

Discussion

This equation can be solved using the following methods:

  • Subtraction Method: Subtract 9 from both sides of the equation to get -4x = 48. Then, divide both sides by -4 to get x = -12.
  • Addition Method: Add 4x to both sides of the equation to get 9 = 57 + 4x. Then, subtract 57 from both sides to get -48 = 4x. Finally, divide both sides by 4 to get x = -12.

Tips and Tricks

  • When solving linear equations, always isolate the variable first.
  • When getting rid of the constant term, make sure to do the same operation to both sides of the equation.
  • When solving for the variable, make sure to divide both sides of the equation by the coefficient of the variable.

Related Topics

  • Linear Equations: Linear equations are equations in which the highest power of the variable is 1.
  • Solving Linear Equations: Solving linear equations involves isolating the variable, getting rid of the constant term, and solving for the variable.
  • Graphing Linear Equations: Graphing linear equations involves plotting the equation on a coordinate plane and identifying the x and y intercepts.

Practice Problems

  • Solve the equation 2x + 5 = 11.
  • Solve the equation x - 3 = 7.
  • Solve the equation 4x - 2 = 14.

Conclusion

Introduction

In our previous article, we demonstrated the step-by-step process of solving a linear equation of the form $ax + b = c$. We used the equation $9 - 4x = 57$ as an example and showed how to isolate the variable, get rid of the constant term, and solve for the variable. In this article, we will provide a Q&A guide to help you better understand and apply the concepts of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable 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 isolate the variable, get rid of the constant term, and solve for the variable. Here's a step-by-step guide:

  1. Isolate the variable by adding or subtracting the same value to both sides of the equation.
  2. Get rid of the constant term by adding or subtracting the same value to both sides of the equation.
  3. Solve for the variable by dividing both sides of the equation by the coefficient 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. For example, the equation $x + 2 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.

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's always a good idea to check your work by plugging the solution 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 isolating the variable first
  • Not getting rid of the constant term
  • Not solving for the variable
  • Not checking your work

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to plot the equation on a coordinate plane and identify the x and y intercepts. Here's a step-by-step guide:

  1. Plot the x and y intercepts on the coordinate plane.
  2. Draw a line through the intercepts.
  3. Label the x and y axes.

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.
  • Engineering: Linear equations are used to design and optimize systems.
  • Economics: Linear equations are used to model economic systems.

Conclusion

In this article, we provided a Q&A guide to help you better understand and apply the concepts of solving linear equations. We covered topics such as the definition of a linear equation, how to solve a linear equation, and common mistakes to avoid. We also discussed how to graph a linear equation and provided some real-world applications of linear equations.

Practice Problems

  • Solve the equation 2x + 5 = 11.
  • Solve the equation x - 3 = 7.
  • Solve the equation 4x - 2 = 14.

Tips and Tricks

  • Always isolate the variable first.
  • Always get rid of the constant term.
  • Always solve for the variable.
  • Always check your work.

Related Topics

  • Linear Equations: Linear equations are equations in which the highest power of the variable is 1.
  • Solving Linear Equations: Solving linear equations involves isolating the variable, getting rid of the constant term, and solving for the variable.
  • Graphing Linear Equations: Graphing linear equations involves plotting the equation on a coordinate plane and identifying the x and y intercepts.

Conclusion

In this article, we provided a Q&A guide to help you better understand and apply the concepts of solving linear equations. We covered topics such as the definition of a linear equation, how to solve a linear equation, and common mistakes to avoid. We also discussed how to graph a linear equation and provided some real-world applications of linear equations.