Sure, let's solve the equation for [tex]\( z \)[/tex] step by step.
The given equation is:
[tex]\[ a \cdot (t + z) = 45z + 67 \][/tex]
Here's the process of solving for [tex]\( z \)[/tex]:
1. Distribute [tex]\( a \)[/tex] on the left-hand side:
[tex]\[ at + az = 45z + 67 \][/tex]
2. Gather all terms involving [tex]\( z \)[/tex] on one side of the equation and constants on the other:
[tex]\[ az - 45z = 67 - at \][/tex]
3. Factor out [tex]\( z \)[/tex] from the left-hand side:
[tex]\[ z(a - 45) = 67 - at \][/tex]
4. Solve for [tex]\( z \)[/tex] by isolating it:
[tex]\[ z = \frac{67 - at}{a - 45} \][/tex]
Therefore, the solution for [tex]\( z \)[/tex] in the given equation is:
[tex]\[ z = \frac{67 - at}{a - 45} \][/tex]
This is the final solution.
