If `k(x)=(2x-p)/(5) and k(7)=3`, what is the value of p?

Answer

To solve the problem step by step, we follow these instructions:

1. **Write down the function**: We are given the function \( k(x) = \frac{2x - p}{5} \).

2. **Substitute the value of x**: Since we know \( k(7) = 3 \), we substitute \( x = 7 \) into the function:
\[ k(7) = \frac{2(7) - p}{5} \]

3. **Set the equation equal to 3**: We know from the problem statement that \( k(7) = 3 \), so we can set up the equation:
\[ \frac{2(7) - p}{5} = 3 \]

4. **Multiply both sides by 5**: To eliminate the fraction, we multiply both sides of the equation by 5:
\[ 2(7) - p = 3 \times 5 \]

5. **Calculate the left side**: Calculate \( 2(7) \) and \( 3 \times 5 \):
\[ 14 - p = 15 \]

6. **Isolate p**: Now, we need to isolate \( p \). We can do this by rearranging the equation:
\[ -p = 15 - 14 \]
\[ -p = 1 \]

7. **Solve for p**: Multiply both sides by -1 to solve for \( p \):
\[ p = -1 \]

Thus, the value of \( p \) is \(-1\).