Solve: $\dfrac{{2 - 9z}}{{17 - 4z}} = \dfrac{4}{5}$

Hint: To solve this type of linear equation we will take variable terms to one side and constants to the other side then we will apply different mathematical operations to get required solution.

Complete step by step answer:
Since given that the equation $\dfrac{{2 - 9z}}{{17 - 4z}} = \dfrac{4}{5}$ and then we need to find the value of the unknown variable $z$, so we will make use of the basic mathematical operations to simplify further.
 Starting with the cross multiplication we have, $\dfrac{{2 - 9z}}{{17 - 4z}} = \dfrac{4}{5} \Rightarrow 5(2 - 9z) = 4(17 - 4z)$
Now by the multiplication operation we get $10 - 45z = 68 - 16z$
now Turing the variables on the left-hand side and also the numbers on the right-hand side we get $10 - 45z = 68 - 16z \Rightarrow 16z - 45z = 68 - 10$ while changing the values on the equals to, the sign of the values or the numbers will change.
By the use of addition and subtraction we get $ - 29z = 58$
Hence by the division, we get $ - 29z = 58 \Rightarrow z = \dfrac{{58}}{{ - 29}} \Rightarrow z = - 2$ which is the required unknown value of the given variable $z$

Note:
There are three methods to solve linear equations in one variable.
1. Trial and Error.
2. Inverse operations.
3. Transposition Method.