Let's solve the equation step-by-step to determine Mia's correctness and see if \( m = 2 \) is indeed the solution.
The original equation is:
\[ 7.8 + 2(0.75m + 0.4) = -6.4m + 4(0.5m - 0.8) \]
First, simplify both sides of the equation.
Starting with the left side:
\[ 7.8 + 2(0.75m + 0.4) = 7.8 + 1.5m + 0.8 = 1.5m + 8.6 \]
Now for the right side:
\[ -6.4m + 4(0.5m - 0.8) = -6.4m + 2m - 3.2 = -4.4m - 3.2 \]
Now we set the two sides equal to each other:
\[ 1.5m + 8.6 = -4.4m - 3.2 \]
Next, we can combine like terms. Add \( 4.4m \) to both sides:
\[ 1.5m + 4.4m + 8.6 = -3.2 \] \[ 6m + 8.6 = -3.2 \]
Now, subtract \( 8.6 \) from both sides:
\[ 6m = -3.2 - 8.6 \] \[ 6m = -11.8 \]
Now, divide by \( 6 \):
\[ m = \frac{-11.8}{6} = -1.96666667 \approx -1.97 \]
So the solution for \( m \) is approximately \( -1.97 \).
Now let's check if \( m = 2 \) gives a true or false statement:
Substituting \( m = 2 \):
Left side:
\[ 7.8 + 2(0.75 \cdot 2 + 0.4) = 7.8 + 2(1.5 + 0.4) = 7.8 + 2(1.9) = 7.8 + 3.8 = 11.6 \]
Right side:
\[ -6.4 \cdot 2 + 4(0.5 \cdot 2 - 0.8) = -12.8 + 4(1 - 0.8) = -12.8 + 4(0.2) = -12.8 + 0.8 = -12 \]
Comparing the two results:
Left side: \( 11.6 \)
Right side: \( -12 \)
Since \( 11.6 \neq -12 \), this means Mia was incorrect.
Thus, the correct explanation is:
She is incorrect because when substituting 2 for m the result was a false statement.
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