To solve the equation [tex]\(\frac{p+1}{2} = \frac{3p+7}{5}\)[/tex] for [tex]\(p\)[/tex], follow these steps:
1. Eliminate the fractions by cross-multiplying:
[tex]\[
5 \cdot (p + 1) = 2 \cdot (3p + 7)
\][/tex]
2. Distribute on both sides:
[tex]\[
5p + 5 = 6p + 14
\][/tex]
3. Move all terms involving [tex]\(p\)[/tex] to one side and constants to the other side:
[tex]\[
5p - 6p = 14 - 5
\][/tex]
4. Simplify the equation:
[tex]\[
-p = 9
\][/tex]
5. Solve for [tex]\(p\)[/tex] by dividing both sides by [tex]\(-1\)[/tex]:
[tex]\[
p = -9
\][/tex]
Thus, the solution to the equation [tex]\(\frac{p+1}{2} = \frac{3p+7}{5}\)[/tex] is:
[tex]\[
p = -9
\][/tex]
