Consider This Equation:$\[ 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) \\]Mia Solved The Equation And Determined That \[$ M = 2 \$\]. Is She Correct?A. She Is Incorrect Because When Substituting 2 For \[$ M \$\], The Result

Introduction

In mathematics, equations are used to represent relationships between variables. Solving an equation involves finding the value of the variable that satisfies the equation. In this article, we will analyze the given equation and determine whether Mia's solution is correct.

The Equation

The given equation is:

${ 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) }$

This equation involves variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Step 1: Distribute the Numbers

To simplify the equation, we need to distribute the numbers outside the parentheses to the terms inside.

${ 7.8 + 2(0.75m) + 2(0.4) = -6.4m + 4(0.5m) - 4(0.8) }$

Step 2: Simplify the Equation

Now, we can simplify the equation by combining like terms.

${ 7.8 + 1.5m + 0.8 = -6.4m + 2m - 3.2 }$

Step 3: Combine Like Terms

We can combine the like terms on both sides of the equation.

${ 8.6 + 1.5m = -4.4m - 3.2 }$

Step 4: Isolate the Variable

To isolate the variable, we need to get all the terms with the variable on one side of the equation.

${ 1.5m + 4.4m = -3.2 - 8.6 }$

Step 5: Combine Like Terms Again

We can combine the like terms on both sides of the equation.

${ 5.9m = -12.8 }$

Step 6: Solve for the Variable

Now, we can solve for the variable by dividing both sides of the equation by the coefficient of the variable.

${ m = \frac{-12.8}{5.9} }$

Mia's Solution

Mia solved the equation and determined that:

${ m = 2 }$

Is Mia Correct?

To determine whether Mia is correct, we need to substitute her solution into the original equation and check if it is true.

${ 7.8 + 2(0.75(2) + 0.4) = -6.4(2) + 4(0.5(2) - 0.8) }$

${ 7.8 + 2(1.5 + 0.4) = -12.8 + 4(1 - 0.8) }$

${ 7.8 + 2(1.9) = -12.8 + 4(0.2) }$

${ 7.8 + 3.8 = -12.8 + 0.8 }$

${ 11.6 = -12 }$

Since the result is not equal to zero, Mia's solution is incorrect.

Conclusion

In conclusion, Mia's solution is incorrect because when substituting 2 for m, the result is not equal to zero. The correct solution involves solving the equation step by step and isolating the variable. By following these steps, we can determine the correct value of the variable.

Final Answer

The final answer is:

${ m = \frac{-12.8}{5.9} }$

Introduction

In our previous article, we analyzed the given equation and determined that Mia's solution was incorrect. In this article, we will provide a step-by-step solution to the equation and answer some frequently asked questions (FAQs) related to the equation.

Step-by-Step Solution

To solve the equation, we need to follow these steps:

1. Distribute the numbers outside the parentheses to the terms inside.
2. Simplify the equation by combining like terms.
3. Isolate the variable by getting all the terms with the variable on one side of the equation.
4. Combine like terms again.
5. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.

Step 1: Distribute the Numbers

To simplify the equation, we need to distribute the numbers outside the parentheses to the terms inside.

${ 7.8 + 2(0.75m) + 2(0.4) = -6.4m + 4(0.5m) - 4(0.8) }$

Step 2: Simplify the Equation

Now, we can simplify the equation by combining like terms.

${ 7.8 + 1.5m + 0.8 = -6.4m + 2m - 3.2 }$

Step 3: Combine Like Terms

We can combine the like terms on both sides of the equation.

${ 8.6 + 1.5m = -4.4m - 3.2 }$

Step 4: Isolate the Variable

To isolate the variable, we need to get all the terms with the variable on one side of the equation.

${ 1.5m + 4.4m = -3.2 - 8.6 }$

Step 5: Combine Like Terms Again

We can combine the like terms on both sides of the equation.

${ 5.9m = -12.8 }$

Step 6: Solve for the Variable

Now, we can solve for the variable by dividing both sides of the equation by the coefficient of the variable.

${ m = \frac{-12.8}{5.9} }$

Q&A

Q: What is the correct solution to the equation? A: The correct solution to the equation is:

${ m = \frac{-12.8}{5.9} }$

Q: Why is Mia's solution incorrect? A: Mia's solution is incorrect because when substituting 2 for m, the result is not equal to zero.

Q: How do I distribute the numbers outside the parentheses to the terms inside? A: To distribute the numbers outside the parentheses to the terms inside, you need to multiply the number outside the parentheses by each term inside the parentheses.

Q: How do I simplify the equation by combining like terms? A: To simplify the equation by combining like terms, you need to add or subtract the coefficients of the like terms.

Q: How do I isolate the variable? A: To isolate the variable, you need to get all the terms with the variable on one side of the equation.

Q: How do I solve for the variable? A: To solve for the variable, you need to divide both sides of the equation by the coefficient of the variable.

Conclusion

In conclusion, solving the equation involves following a series of steps, including distributing the numbers outside the parentheses to the terms inside, simplifying the equation by combining like terms, isolating the variable, combining like terms again, and solving for the variable. By following these steps, we can determine the correct value of the variable.

Final Answer

The final answer is:

${ m = \frac{-12.8}{5.9} }$

This is the correct solution to the equation.