Let's solve each literal equation for the specified variable:
1. Solve \( y = x + 12 \) for \( x \)
To isolate \( x \), we can subtract 12 from both sides:
\[ y - 12 = x \]
So, the solution is:
\[ x = y - 12 \]
2. Solve \( n = \frac{4}{5}(m + 7) \) for \( m \)
To solve for \( m \), we first multiply both sides by \( \frac{5}{4} \) to eliminate the fraction:
\[ \frac{5}{4} n = m + 7 \]
Next, we isolate \( m \) by subtracting 7 from both sides:
\[ \frac{5}{4} n - 7 = m \]
So, the solution is:
\[ m = \frac{5}{4} n - 7 \]
Using the equation from part b to find \( m \) when \( n = 40 \)
Now we substitute \( n = 40 \) into the equation we found for \( m \):
\[ m = \frac{5}{4}(40) - 7 \]
Calculating \( \frac{5}{4}(40) \):
\[ \frac{5 \times 40}{4} = \frac{200}{4} = 50 \]
Now substituting back into the equation for \( m \):
\[ m = 50 - 7 = 43 \]
So, the final answer is:
\[ m = 43 \]