To solve the linear equation 3x = 2x + 18, first isolate the variable x on one side by subtracting 2x from both sides. This simplifies the equation to 3x - 2x = 18, which further reduces to x = 18. Checking the result by substituting 18 back into the original equation gives 3(18) = 2(18) + 18, confirming that 54 = 36 + 18.