Question

Solve each literal equation for the given variable.

y = x + 12; x
n = 4/5(m+7); m

Use your equation from part b to find m when n = 40

Answer 1

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:

\[
m = 43
\]