Respuesta :
- P ( 51 + z ) = dz + 84
First we divide both sides of the equation by -P.
[tex]\begin{gathered} \frac{-P(51+z)}{-P}=\frac{dz}{-P}+\frac{84}{-P} \\ 51+z=\frac{dz}{-P}+\frac{84}{-P} \\ 51+z=-\frac{dz}{P}-\frac{84}{P} \end{gathered}[/tex]Now, we transpose all the terms with the variable z on the left side of the equation, and the constants on the right., and
[tex]\begin{gathered} 51+z=-\frac{dz}{P}-\frac{84}{P} \\ z+\frac{dz}{P}=-\frac{84}{P}-51 \end{gathered}[/tex]Then we'll add the terms on the left and on the right side of the equation.
[tex]\begin{gathered} z+\frac{dz}{P}=-\frac{84}{P}-51 \\ \frac{zP+dz}{P}=\frac{-84-51P}{P} \\ \end{gathered}[/tex]We can cross out the denominator P, since it appears on both sides of the equation. The resulting equation is:
[tex]\begin{gathered} zP+dz=84-51P \\ \end{gathered}[/tex]We have to factor out z on the left, so we can come up with an expression for z
[tex]z(P+d)=84-51P[/tex]Then we divide both sides of the equation by ( P + d )
[tex]\begin{gathered} z(P+d)=84-51P \\ \frac{z(P+d)}{(P+d)}=\frac{84-51P}{(P+d)} \\ z=\frac{84-51P}{(P+d)} \end{gathered}[/tex]Answer:
[tex]z=\frac{84-51P}{(P+d)}[/tex]