Question

Determine whether the given equation has one solution, no solution, or infinitely many solutions: 4x+10=2(2x+5)

Answer 1

if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.

and since  4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.