These equations were nightmares. They looked like this:
[ 5x - 2(3x - 4) = 8 - (x + 6) ]
Left: (-x + 8) Right: (2 - x)
[ 4(2x - 5) - 3(x + 2) = 7x - (2x + 8) ] lesson 3.4 solving complex 1-variable equations
[ -x + 8 = 2 - x ]
Combine like terms:
Epilogue: Kael later became a teacher, and his first lesson was always the same: “When the equation looks like a monster, remember the Four Steps. Fractions first. Then distribute. Then move. Then solve. Always in that order.” These equations were nightmares
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."
He distributed carefully:
From earlier cleared fraction problem: (8x - 4 + 3x = 10x + 4) → (11x - 4 = 10x + 4) Then distribute
Left side: (5x - 6x + 8) (because (-2 \times -4 = +8))
He found the LCD of 3, 4, and 6. That was 12.