Answer: To have infinitely many solutions, the equation must simplify to a true statement, such as 0=0.
So, let's simplify the given equation:
4(x-4) = 4x + ?
We need to choose a value for the constant on the right-hand side so that the equation simplifies to a true statement.
We can start by distributing the 4 on the left-hand side:
4x - 16 = 4x + ?
Now we can see that the 4x terms cancel out, leaving:
-16 = ?
We can choose any value for the constant on the right-hand side, and the equation will be true. For example:
-16 = -16
So the complete equation with infinitely many solutions is:
4(x-4) = 4x - 16
Explanation: