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stira [4]
3 years ago
12

−p(51+z)=dz+84 solve for z

Mathematics
2 answers:
ryzh [129]3 years ago
8 0

Answer:

\boxed{\sf z =  \frac{ - 51p  -  84}{  p  +  d} \ \ \  OR \ \ \ z = - \frac{51p  + 84}{  p  +  d} }

Step-by-step explanation:

\sf  solve \:  for  \: z :  \\  \sf \implies −p(51+z)=dz+84 \\  \\  \sf Expand \:  out \:  terms \:  of  \: the \:  left \:  hand  \: side: \\  \sf \implies  - 51p - pz = dz + 84  \\  \\ \sf Subtract  \: d z  - 51 p \:  from \:  both  \: sides:  \\ \sf \implies - 51p - pz  - (dz - 51p)= dz + 84 - (dz - 51p) \\ \\   \sf  - (dz - 51p) =  - dz + 51p :   \\ \sf \implies - 51p - pz  - dz  +  51p= dz + 84 - dz  +  51p  \\  \\ \sf  - 51p + 51p = 0 : \\   \sf \implies  - pz  - dz = dz + 84 - dz +  51p \\  \\  \sf dz - dz = 0 :  \\  \sf \implies  - pz  - dz =  84  +  51p \\  \\  \sf \implies   z( - p    -   d) =  84  +  51p \\  \\  \sf Divide  \: both  \: sides  \: by  \:  - p - d: \\  \sf \implies z =  \frac{51p + 84}{ - p - d}  \\  \\  \sf \implies z =  \frac{51p + 84}{ -( p  + d)}  \\  \\  \sf \implies z =  \frac{ - (51p + 84)}{ p  +  d}  \\  \\  \sf \implies z =  \frac{ - 51p  -  84}{  p  +  d}

tiny-mole [99]3 years ago
6 0

\text{Solve for z:}\\\\-p(51+z)=dz+84\\\\\text{Use the distributive property}\\\\-51p-pz=dz+84\\\\\text{Add 51p to both sides}\\\\-pz=51p+dz+84\\\\\text{Subtract dz from both sides}\\\\-pz-dz=51p+84\\\\\text{Factor out z}\\\\z(-d-p)=51p+84\\\\\text{Divide both sides by (-d - p)}\\\\z=\frac{51p+84}{(-d-p)}\\\\\text{The denominator shouldn't be zero, so we have to make it positive}\\\\\boxed{z=\frac{-51p-84}{d+p}\,\,or\,\,z=-\frac{51p+84}{d+p}}

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