Answer:
30
Step-by-step explanation:
Let us divide the whole expression by 5. Then we must multiply the whole expression by 5 to obtain the same value as before.
Thus, we get the following expression:
![\implies\huge\text{[}\dfrac{5(z+4)+5(2-z)}{5}\huge\text{]} \times 5](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7B5%28z%2B4%29%2B5%282-z%29%7D%7B5%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205)
![\implies\huge\text{[}\dfrac{(z+4)+(2-z)}{1}\huge\text{]} \times 5](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7B%28z%2B4%29%2B%282-z%29%7D%7B1%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205)
Now, open the inner-most parentheses as the expression inside the inner-most parentheses, cannot be simplified further.
![\implies\huge\text{[}\dfrac{z+4+2-z}{1}\huge\text{]} \times 5](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7Bz%2B4%2B2-z%7D%7B1%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205)
It should be noted that any number being subtracted from the same number is equivalent to 0. Therefore, we get the following expression:
![\implies\huge\text{[}\dfrac{4+2}{1}\huge\text{]} \times 5](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7B4%2B2%7D%7B1%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205)
Simplify the expression inside the long brackets.
![\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7B6%7D%7B1%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205)
Now, we can open the long brackets and simplify the product of 6/1 and 5.
![\implies\huge\text{[}\dfrac{6}{1}\huge\text{]} \times 5 = \dfrac{6 \times 5}{1} = \dfrac{30}{1} = 30](https://tex.z-dn.net/?f=%5Cimplies%5Chuge%5Ctext%7B%5B%7D%5Cdfrac%7B6%7D%7B1%7D%5Chuge%5Ctext%7B%5D%7D%20%5Ctimes%205%20%3D%20%5Cdfrac%7B6%20%5Ctimes%205%7D%7B1%7D%20%20%3D%20%5Cdfrac%7B30%7D%7B1%7D%20%3D%2030)
Therefore, the simplified expression is 30.
Learn more about one-variable expressions: brainly.com/question/27721172