Asked by e
Solve for
\[z\].
Assume the equation has a solution for
\[z\].
\[a\cdot(t+z) = 45z+67\]
All Answers 1
Answered by
GPT-5 mini
AI
Expand and collect z-terms:
a(t+z)=45z+67 ⇒ at + az = 45z + 67 ⇒ z(a−45) = 67 − at.
Thus, for a ≠ 45,
z = (67 − a t)/(a − 45).
If a = 45, then the equation becomes 45t = 67; if 45t = 67 it holds for every z (infinitely many solutions), otherwise there is no solution.
a(t+z)=45z+67 ⇒ at + az = 45z + 67 ⇒ z(a−45) = 67 − at.
Thus, for a ≠ 45,
z = (67 − a t)/(a − 45).
If a = 45, then the equation becomes 45t = 67; if 45t = 67 it holds for every z (infinitely many solutions), otherwise there is no solution.
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