How do you simplify $ - \dfrac{1}{2}\left( {7z + 4} \right) + \dfrac{1}{5}\left( {5z - 16} \right)?$

Hint: In this question, we are going to simplify the given equation.
First, we are going to simplify the given equation by expanding the given terms.
Then combine the like terms by getting the common denominator.
Hence, we can get the required result.

Complete step-by-step solution:
In this question, we are going to simplify the given equation.
First write the given equation
$ \Rightarrow - \dfrac{1}{2}\left( {7z + 4} \right) + \dfrac{1}{5}\left( {5z - 16} \right)$
Now, we are going to simplify the given equation by expanding the given terms.
$ \Rightarrow - \dfrac{1}{2}\left( {7z} \right) - \left( {\dfrac{1}{2}\left( 4 \right)} \right) + \dfrac{1}{5}\left( {5z} \right) - \dfrac{1}{5}\left( {16} \right)$
Now we are going to combine the like terms by getting the common denominator.
$ \Rightarrow - \dfrac{{7z}}{2} - \left( {\dfrac{4}{2}} \right) + \dfrac{{5z}}{5} - \dfrac{{16}}{5}$
Simplifying the above term we get,
$ \Rightarrow \dfrac{{ - 7z}}{2} + z - 2 - \dfrac{{16}}{5}$
Taking LCM for the above equation,
$ \Rightarrow \dfrac{{ - 7z + 2z}}{2} + \dfrac{{ - 10 - 16}}{5}$
Let us add the term and we get
$ \Rightarrow \dfrac{{ - 5z}}{2} - \dfrac{{26}}{5}$
On rewriting the term and we get
$ \Rightarrow \dfrac{{ - 5z}}{2} = \dfrac{{26}}{5}$
Then we get,
$ \Rightarrow - z = \dfrac{{26}}{5} \times \dfrac{2}{5}$
On cancel the term and we get,
$ \Rightarrow z = - \dfrac{{52}}{{25}}$
On divide the term and we get
$ \Rightarrow z = - 2.08$

Therefore the value of z when equated to zero is -2.08.

Note: Simplification of an algebraic expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.
Let us remind ourselves some of the important terms used when simplifying an expression:
A variable is a letter whose value is unknown.
The coefficient is a numerical value used together with a variable.
A constant is a term which has a definite value.
Like terms are variable with same letter and power
The following are the basic rules and steps to simplify an expression:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.
Use the exponent rule to remove the grouping if the terms are containing exponents.
Combine the like terms by addition or subtraction.
Combine the constants.