The ICE Table Method
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Solving an equilibrium problem with an ICE table means recording each species' Initial concentration, its Change expressed as a multiple of an unknown x using stoichiometric coefficients, and the resulting Equilibrium concentration, then substituting the equilibrium row into the K expression and solving for x.
For H2 + I2 ⇌ 2 HI, K = 54.3, starting from 1.00 M each of H2 and I2 and no HI, the ICE table gives equilibrium concentrations (1.00 − x), (1.00 − x), and 2x. Substituting into K = (2x)²/[(1.00 − x)(1.00 − x)] and solving yields x ≈ 0.786, so [HI] at equilibrium is about 1.57 M.
Forgetting that a coefficient of 2 multiplies x in the Change row, not only in the Equilibrium row, produces equilibrium concentrations that do not satisfy the balanced equation.