Question

Does the equation 3(x-2)=3x-2 have one solution, no solution or an infinite number of solutions?

Answer 1

If you expand the left hand sign, the equation becomes

$3x-6 = 3x-2$

This means that the term $3x$ cancels out, since it appears in both sides. So, we're left with

$-6=-2$

which is clearly false, i.e. it leads to an impossible equation, which thus have no solutions.