Solve For $x$:$3x = 57$A. \$x = 57$[/tex\] B. $x = 54$ C. $x = 60$

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 simple linear equation of the form $ax = b$, where $a$ and $b$ are constants. We will use the equation $3x = 57$ as an example to demonstrate the step-by-step process of solving for $x$.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$) is 1. Linear equations can be written in the form $ax = b$, where $a$ and $b$ are constants. The variable $x$ is the unknown quantity that we are trying to solve for.

The Equation $3x = 57$

The equation $3x = 57$ is a simple linear equation in which the coefficient of $x$ is 3, and the constant term is 57. Our goal is to solve for $x$ by isolating it on one side of the equation.

Step 1: Divide Both Sides by 3

To solve for $x$, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 3. This will cancel out the coefficient of $x$, which is 3.

$$\frac{3x}{3} = \frac{57}{3}$$

Step 2: Simplify the Equation

After dividing both sides by 3, we get:

$$x = 19$$

Conclusion

In this article, we solved the linear equation $3x = 57$ by dividing both sides by 3 and simplifying the equation. We found that the solution to the equation is $x = 19$. This is the value of $x$ that satisfies the equation.

Why is Solving Linear Equations Important?

Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, linear equations are used to describe the motion of objects, while in economics, they are used to model the behavior of markets. In computer science, linear equations are used to solve systems of equations and optimize algorithms.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. These include:

• Dividing by zero: This is a common mistake that can occur when solving linear equations. To avoid this, make sure to check if the coefficient of $x$ is zero before dividing both sides by it.
• Not simplifying the equation: After dividing both sides by the coefficient of $x$, make sure to simplify the equation to find the solution.
• Not checking the solution: After finding the solution, make sure to check if it satisfies the original equation.

Real-World Applications of Solving Linear Equations

Solving linear equations has numerous real-world applications. Some examples include:

• Physics: Linear equations are used to describe the motion of objects. For example, the equation $v = u + at$ describes the velocity of an object as a function of time.
• Economics: Linear equations are used to model the behavior of markets. For example, the equation $p = mc + b$ describes the price of a good as a function of its cost and demand.
• Computer Science: Linear equations are used to solve systems of equations and optimize algorithms. For example, the equation $Ax = b$ describes a system of linear equations, where $A$ is a matrix, $x$ is a vector of variables, and $b$ is a vector of constants.

Conclusion

In this article, we solved the linear equation $3x = 57$ by dividing both sides by 3 and simplifying the equation. We found that the solution to the equation is $x = 19$. Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. By following the step-by-step process outlined in this article, you can solve linear equations with confidence.

Final Answer

Introduction

In our previous article, we discussed the basics of solving linear equations and provided a step-by-step guide on how to solve the equation $3x = 57$. 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. Linear equations can be written in the form $ax = b$, where $a$ and $b$ are constants.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable (in this case, $x$) on one side of the equation. You can do this by performing the following steps:

1. Divide both sides by the coefficient of $x$: If the coefficient of $x$ is not 1, divide both sides of the equation by it.
2. Simplify the equation: After dividing both sides by the coefficient of $x$, simplify the equation to find the solution.

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 is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x = 6$ is a linear equation.

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

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your work by hand to make sure that the solution is correct.

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

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

• Dividing by zero: This is a common mistake that can occur when solving linear equations. To avoid this, make sure to check if the coefficient of $x$ is zero before dividing both sides by it.
• Not simplifying the equation: After dividing both sides by the coefficient of $x$, make sure to simplify the equation to find the solution.
• Not checking the solution: After finding the solution, make sure to check if it satisfies the original equation.

Q: How do I check if a solution satisfies the original equation?

A: To check if a solution satisfies the original equation, plug the solution back into the equation and make sure that it is true. For example, if the solution to the equation $2x = 6$ is $x = 3$, plug $x = 3$ back into the equation and make sure that it is true: $2(3) = 6$.

Q: Can I use linear equations to solve systems of equations?

A: Yes, you can use linear equations to solve systems of equations. A system of equations is a set of two or more equations that are all true at the same time. To solve a system of equations, you can use the following methods:

• Substitution method: This method involves substituting the solution to one equation into the other equation to find the solution to the system.
• Elimination method: This method involves adding or subtracting the equations to eliminate one of the variables and find the solution to the system.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. We discussed the basics of linear equations, how to solve them, and some common mistakes to avoid. We also discussed how to check if a solution satisfies the original equation and how to use linear equations to solve systems of equations.

Final Answer

The final answer is: $\boxed{19}$