Question

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?
She is incorrect because when substituting 2 for m the result was a true statement.
She is incorrect because when substituting 2 for m the result was a false statement.
She is correct because when substituting 2 for m the result was a true statement.
She is correct because when substituting 2 for m the result was a false statement.

Answer 1

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.**