Solve The Equation.${ \begin{array}{l} 5=\frac{g}{8} \ g=\square \end{array} }$

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Introduction

In mathematics, equations are a fundamental concept that help us understand and describe the world around us. Solving equations is a crucial skill that enables us to find the value of unknown variables, which is essential in various fields such as science, engineering, and economics. In this article, we will focus on solving a simple equation involving a variable g, and uncover its value.

The Equation

The given equation is:

5=g8g=â–¡\begin{array}{l} 5=\frac{g}{8} \\ g=\square \end{array}

This equation states that the value of 5 is equal to the variable g divided by 8. Our goal is to solve for the value of g.

Step 1: Multiply Both Sides by 8

To solve for g, we need to isolate the variable g on one side of the equation. We can do this by multiplying both sides of the equation by 8, which is the denominator of the fraction.

5×8=g8×85 \times 8 = \frac{g}{8} \times 8

This simplifies to:

40=g40 = g

Step 2: Solve for g

Now that we have multiplied both sides of the equation by 8, we can see that the value of g is equal to 40.

Conclusion

In this article, we have solved the equation 5=g8g=â–¡\begin{array}{l} 5=\frac{g}{8} \\ g=\square \end{array} and uncovered the value of g. By multiplying both sides of the equation by 8, we were able to isolate the variable g and find its value. The final answer is:

g = 40

Real-World Applications

Solving equations like this one has numerous real-world applications. For example, in physics, equations are used to describe the motion of objects, and solving them helps us understand the behavior of the objects. In economics, equations are used to model the behavior of markets, and solving them helps us understand the impact of different variables on the market.

Tips and Tricks

When solving equations, it's essential to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following these steps, you can ensure that you are solving equations correctly and efficiently.

Common Mistakes

When solving equations, it's easy to make mistakes. Here are some common mistakes to watch out for:

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect solutions.
  • Not isolating the variable: Failing to isolate the variable on one side of the equation can make it difficult to solve.
  • Not checking the solution: Failing to check the solution can lead to incorrect answers.

Conclusion

Q&A: Frequently Asked Questions

Q: What is the equation we are trying to solve? A: The equation we are trying to solve is 5=g8g=â–¡\begin{array}{l} 5=\frac{g}{8} \\ g=\square \end{array}, where we need to find the value of g.

Q: Why do we need to multiply both sides of the equation by 8? A: We need to multiply both sides of the equation by 8 to isolate the variable g on one side of the equation. This is because the variable g is currently divided by 8, and we need to get rid of the denominator to solve for g.

Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when solving an equation. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some common mistakes to watch out for when solving equations? A: Some common mistakes to watch out for when solving equations include:

  • Not following the order of operations
  • Not isolating the variable
  • Not checking the solution

Q: How do I check my solution to make sure it is correct? A: To check your solution, you can plug the value of g back into the original equation and see if it is true. If the equation is true, then your solution is correct.

Q: What are some real-world applications of solving equations? A: Solving equations has numerous real-world applications, including:

  • Physics: Equations are used to describe the motion of objects, and solving them helps us understand the behavior of the objects.
  • Economics: Equations are used to model the behavior of markets, and solving them helps us understand the impact of different variables on the market.

Q: Can you give me an example of a real-world equation that I might encounter? A: Here is an example of a real-world equation:

2x+5=11x=â–¡\begin{array}{l} 2x + 5 = 11 \\ x = \square \end{array}

To solve for x, we can subtract 5 from both sides of the equation and then divide both sides by 2.

Q: How do I know which operations to perform first when solving an equation? A: To determine which operations to perform first, you can follow the order of operations (PEMDAS). This will tell you which operations to perform first, and in what order.

Q: Can you give me some tips for solving equations? A: Here are some tips for solving equations:

  • Follow the order of operations (PEMDAS)
  • Isolate the variable on one side of the equation
  • Check your solution to make sure it is correct
  • Use a calculator or computer to check your solution if necessary

Conclusion

Solving equations is a fundamental skill in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can solve equations like this one and uncover the value of unknown variables. Remember to follow the order of operations, isolate the variable, and check your solution to ensure that you are solving equations correctly and efficiently.