What Steps Are Used To Solve This Equation?$\[ 6f = 48 \\]Complete Each Statement.First, \[$\square\$\] On Both Sides Of The Equation.Next, Simplify The Equation To Determine That The Solution Of The Equation Is

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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 explore the steps used to solve a linear equation, using the equation 6f = 48 as an example. By following these steps, you will be able to solve linear equations with ease and confidence.

Step 1: Isolate the Variable

The first step in solving a linear equation is to isolate the variable. In the equation 6f = 48, the variable is f. To isolate f, we need to get rid of the coefficient 6 that is being multiplied by f.

Divide Both Sides of the Equation

To isolate f, we need to divide both sides of the equation by 6. This will cancel out the coefficient 6 and leave us with f on its own.

6f = 48
f = 48 ÷ 6
f = 8

Simplify the Equation

By dividing both sides of the equation by 6, we have simplified the equation and isolated the variable f. The solution to the equation is f = 8.

Step 2: Check the Solution

Once we have solved the equation, it's essential to check our solution to ensure that it is correct. We can do this by plugging the solution back into the original equation and checking if it is true.

Plug the Solution Back into the Equation

Let's plug f = 8 back into the original equation 6f = 48.

6(8) = 48
48 = 48

Verify the Solution

As we can see, the solution f = 8 satisfies the original equation 6f = 48. Therefore, our solution is correct.

Conclusion

Solving linear equations is a straightforward process that involves isolating the variable and simplifying the equation. By following the steps outlined in this article, you will be able to solve linear equations with ease and confidence. Remember to always check your solution to ensure that it is correct.

Common Mistakes to Avoid

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

  • Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
  • Not simplifying the equation: Failing to simplify the equation can make it difficult to solve.
  • Not checking the solution: Failing to check the solution can lead to incorrect answers.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use inverse operations: Inverse operations are operations that "undo" each other. For example, addition and subtraction are inverse operations, as are multiplication and division.
  • Use the order of operations: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).
  • Check your solution: Always check your solution to ensure that it is correct.

Real-World Applications

Linear equations have numerous real-world applications. Some examples include:

  • Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Conclusion

Introduction

In our previous article, we explored the steps used to solve a linear equation, using the equation 6f = 48 as an example. 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 is 1. In other words, it is an equation in which the variable is not raised to a power greater than 1.

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

A: The first step in solving a linear equation is to isolate the variable. This involves getting rid of any coefficients or constants that are being added to or subtracted from the variable.

Q: How do I isolate the variable?

A: To isolate the variable, you need to use inverse operations. For example, if the variable is being multiplied by a coefficient, you can divide both sides of the equation by that coefficient to isolate the variable.

Q: What is an inverse operation?

A: An inverse operation is an operation that "undoes" another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use the order of operations to solve a linear equation?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). When solving a linear equation, you should follow the order of operations to ensure that you are performing the operations in the correct order.

Q: Why is it important to check my solution?

A: It is essential to check your solution to ensure that it is correct. If you do not check your solution, you may end up with an incorrect answer.

Q: How do I check my solution?

A: To check your solution, you need to plug the solution back into the original equation and check if it is true. If the solution satisfies the original equation, then it 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:

  • Not isolating the variable
  • Not simplifying the equation
  • Not checking the solution

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

A: Linear equations have numerous real-world applications, including:

  • Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
  • Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: Can you provide some examples of linear equations?

A: Here are some examples of linear equations:

  • 2x + 3 = 5
  • x - 2 = 7
  • 4y = 12

Q: How do I solve a linear equation with a variable on both sides?

A: To solve a linear equation with a variable on both sides, you need to use inverse operations to isolate the variable. For example, if the equation is 2x + 3 = 5, you can subtract 3 from both sides to get 2x = 2, and then divide both sides by 2 to get x = 1.

Conclusion

Solving linear equations is a fundamental skill that has numerous real-world applications. By following the steps outlined in this article, you will be able to solve linear equations with ease and confidence. Remember to always check your solution to ensure that it is correct.