Kael checked it in the original fraction equation. It worked. The numbers aligned. The universe hummed. On trial day, Arch-Mathemagician Prime presented the final challenge:
Left: (-x + x + 8 = 8) Right: (2 - x + x = 2) lesson 3.4 solving complex 1-variable equations
Add (x) to both sides:
And this:
Kael froze. That was false. No solution? He checked his work. Then he remembered: if you eliminate variables and get a false statement (like (8=2)), the equation has . If you get a true statement (like (5=5)), it has infinitely many solutions . Kael checked it in the original fraction equation
He multiplied (yes, even the lonely ( + \frac{x}{4} )) by 12: lesson 3.4 solving complex 1-variable equations