From (-x + 8 = 2 - x):
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 . lesson 3.4 solving complex 1-variable equations
But Kael had a secret weapon: an old, dusty scroll from his grandmother, a former Keeper of the Balance. It was titled Step 1: Clear the Denominators (The Great Purge) Kael’s grandmother’s scroll read: “Fractions are fear made visible. Eliminate them by multiplying every term by the Least Common Denominator (LCD).” From (-x + 8 = 2 - x): Kael froze
Now: (8 = 2)
He found the LCD of 3, 4, and 6. That was 12. He checked his work
[ \frac{3(x - 4)}{2} + 5 = \frac{2x + 1}{3} - 4 ]