Lesson 3.4 Solving Complex 1-variable Equations < QUICK TIPS >

Our hero, a young apprentice named , had failed the trial twice. His first attempt ended when he saw ( \frac{x}{2} + \frac{x}{3} = 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."

In the floating city of Veritas-Algebra, there was a strict law: every citizen must pass the Trial of the Single Variable to earn their adult sigil. The problem was that the trial had changed. No longer were there simple equations like (2x + 3 = 7). The new Arch-Mathemagician, a stern woman named Prime, had introduced . lesson 3.4 solving complex 1-variable equations

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: Our hero, a young apprentice named , had

Left: (-x + 8) Right: (2 - x)

Kael moved to a second problem: