Lesson 3.4 Solving Complex 1-variable Equations -

No solution. This equation is inconsistent. Some complex equations lead to ( 0 = 5 ) (none) or ( 0=0 ) (infinite solutions).

Our hero, a young apprentice named , had failed the trial twice. His first attempt ended when he saw ( \fracx2 + \fracx3 = 10 ) and froze like a rabbit in torchlight. His second attempt ended when he tried to "move everything to the other side" without a plan and ended up with (x = x), which Arch-Mathemagician Prime called "an infinite tautology of shame."

( 2x + 1 = 9 ) → ( 2x = 8 ) → ( x = 4 )

While most equations have one solution, complex equations can result in two unique outcomes:

[ \frac3(x - 4)2 + 5 = \frac2x + 13 - 4 ]