Answer: The required value of z is \(\dfrac{4}{3}.\)
Step-by-step explanation: We are given to solve the following equation for z :
\(z-\dfrac{4}{9}-\dfrac{1}{3}=\dfrac{5}{9}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
To solve the given equation for z, we need to take all the constant terms on the right-hand side of the equation.
From equation (i), we have
\(z-\dfrac{4}{9}-\dfrac{1}{3}=\dfrac{5}{9}\\\\\\\Rightarrow z=\dfrac{5}{9}+\dfrac{1}{3}+\dfrac{4}{9}\\\\\\\Rightarrow z=\dfrac{5+3+4}{9}\\\\\\\Rightarrow z=\dfrac{12}{9}\\\\\Rightarrow z=\dfrac{4}{3}.\)
Thus, the required value of z is \(\dfrac{4}{3}.\)
