Answer:
The completed equation must be 4x + 7 = 4(x + 3) – 5
Explanation:
For this equation to have infinitely many solutions, we must solve for x and reach a point where we have "0x = 0".
Notice that, x = ... -2, -1, 0, 1, 2 ... are all solutions of "0x = 0".
We will call the missing term "t", then the given equations is...
4x + 7 = 4(x + 3) – t
We distribute 4 over the parentheses on right side...
4x + 7 = 4x + 12 – t
We substract 7 on both sides...
4x + 7 - 7 = 4x + 12 – t - 7
4x = 4x + 5 – t
We substract 4x on both sides...
4x - 4x = 4x + 5 – t - 4x
0x = 5 - t
As state above, this equation will have infinitely many solutions if the right side is 0...
5 - t = 0
5 = t