While crossing a remote mountain pass, Emek and Tara found the safe trail blocked by a locked gate. A marker beside it explained that the gate code was the value of x satisfying 4(2x - 3) + 7 = 3(x + 5) + 20. Tara expanded both sides, obtaining 8x - 5 = 3x + 35. Emek suggested collecting the variable terms first. Subtracting 3x from both sides gave 5x - 5 = 35, and adding 5 gave 5x = 40. They found x = 8, but Tara insisted on checking before entering the code. In the original equation, the left side became 4(16 - 3) + 7 = 59, while the right side became 3(8 + 5) + 20 = 59. Since both sides matched, Emek entered 8. The gate unlocked, allowing them to continue along the protected trail before the mountain weather changed.