Question

−p(51+z)=dz+84 solve for z

Answer 1

`\boxed{\sf z = ( - 51p - 84)/( p + d) \ \ \ OR \ \ \ z = - (51p + 84)/( p + d) }`

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 = (51p + 84)/( - p - d) \\ \\ \sf \implies z = (51p + 84)/( -( p + d)) \\ \\ \sf \implies z = ( - (51p + 84))/( p + d) \\ \\ \sf \implies z = ( - 51p - 84)/( p + d)`

Answer 2

`\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=(51p+84)/((-d-p))\\\\\text{The denominator shouldn't be zero, so we have to make it positive}\\\\\boxed{z=(-51p-84)/(d+p)\,\,or\,\,z=-(51p+84)/(d+p)}`