Question

Determine whether the given equation has one solution, no solution, or infinitely many solutions.

2 - 3(x + 4) = 3(3 - x)

cannot be determined
one solution
no solution
infinitely many solutions

Answer 1

Perform the indicated multiplication: 2 - 3x - 12 = 9 - 3x

Gather all the x terms on one side and all the constants on the other:

-3x + 3x = 9 + 12 - 2, or 0 = 19

since this is never true, 2 - 3x - 12 = 9 - 3x has no solution.