Final answer:
To make the equation 25x + 1 = 7 + 3 + 25x have infinitely many solutions, the constant terms on both sides must be equal, resulting in the equation 25x + 10 = 10 + 25x.
Step-by-step explanation:
To complete the equation so that it has infinitely many solutions, you must ensure that both sides of the equation are identical. The equation given is 25x + 1 = 7 + 3 + 25x.
First, simplify both sides of the equation. On the right side, combine like terms: 7 + 3 = 10. So now the equation looks like 25x + 1 = 10 + 25x.
To have infinitely many solutions, the equation has to be true for all values of x. This requires that the non-variable terms on both sides are equal.
Therefore, we must make the constant term on the left side equal to the constant term on the right side, which means setting 1 equal to 10.
The completed equation that has infinitely many solutions is 25x + 10 = 10 + 25x.