Answer:
The value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.
Step-by-step explanation:
Given the expression

solving


We know that the equations with infinitely many solutions have the same expressions on both sides
It means the value of k can be determined by further simplifying such as

8x+20-8x = k
20 = k
Therefore, the value of k = 20 for equation 2(4x+10)=8x+k to have infinitely many solutions.
VERIFICATION:
Given


Put k = 20 in the equation



equations with infinitely many solutions have the same expressions on both sides.
This means the statement is always true.