Answer:
The youngest brother's age is 21 years.
Step-by-step explanation:
Given:
The ages of 3 brothers are consecutive integers.
If the oldest brothers age is decreased by twice the youngest brother age the result is -19
To find the age of the youngest brother.
Solution:
Let the age of youngest broth be =
years
The ages are consecutive integers.
So, age of the next older brother will be =
years
The age of the oldest brother will be =
years
The oldest brothers age is decreased by twice the youngest brother age.
The above statement can be represented as:
⇒ 
Simplifying.
⇒ 
⇒
The result for the above expression = -19.
So, we have:

Subtracting both sides by 2.


Multiplying both sides by -1.
∴ 
Thus, the youngest brother's age is 21 years