To solve the given proportion:
[tex]\[
\frac{P+10}{P-7} = \frac{8}{9}
\][/tex]
we can follow these steps:
1. Cross-multiply to eliminate the fractions:
[tex]\[
9(P + 10) = 8(P - 7)
\][/tex]
2. Distribute the coefficients on both sides:
[tex]\[
9P + 90 = 8P - 56
\][/tex]
3. Move all terms involving [tex]\(P\)[/tex] to one side and constant terms to the other side:
[tex]\[
9P - 8P = -56 - 90
\][/tex]
4. Simplify both sides:
[tex]\[
P = -146
\][/tex]
Since we need to round to the nearest hundredth if necessary, our final answer will be:
[tex]\[
-146.00
\][/tex]
Therefore, [tex]\(P\)[/tex] is:
[tex]\[
\boxed{-146}
\][/tex]
