Questions: Solve the equation for P. N = (9/7)P + 26 P = □ (Simplify your answer.)

Transcript text: Solve the equation for P . \[ \begin{array}{l} \mathrm{N}=\frac{9}{7} \mathrm{P}+26 \\ \mathrm{P}=\square \end{array} \] (Simplify your answer.)

Solution

Solution Steps

To solve for \( P \) in the equation \( N = \frac{9}{7}P + 26 \), we need to isolate \( P \) on one side of the equation. This involves subtracting 26 from both sides and then multiplying both sides by the reciprocal of \(\frac{9}{7}\), which is \(\frac{7}{9}\).

Step 1: Rearranging the Equation

We start with the equation given by \( N = \frac{9}{7}P + 26 \). To isolate \( P \), we first subtract 26 from both sides:

\[ N - 26 = \frac{9}{7}P \]

Step 2: Isolating \( P \)

Next, we multiply both sides by the reciprocal of \( \frac{9}{7} \), which is \( \frac{7}{9} \):

\[ P = \frac{7}{9}(N - 26) \]

Step 3: Simplifying the Expression

Distributing \( \frac{7}{9} \) gives us:

\[ P = \frac{7}{9}N - \frac{7}{9} \times 26 \]

Calculating \( \frac{7 \times 26}{9} \) results in:

\[ \frac{182}{9} \]

Thus, we can express \( P \) as: