4 1/2z+7/9z + 2 1/3 + 1/6z=5 1/18

4 1/2 * z + 7/9 * z + 2 1/3 + 1/6 * z = 5 1/18;

(4 * 2 + 1)/2 * z + 7/9 * z + (2 * 3 + 1)/3 + 1/6 * z = (5 * 18 + 1)/18;

9/2 * z + 7/9 * z + 7/3 + 1/6 * z = 91/18;

81/18 * z + 14/18 * z + 3/18 * z = 91/18 - 42/18;

(81 + 14 + 3)/18 * z = (91 - 42)/18;

98/18 * z = 49/18;

98 * z = 49;

z = 49/98 = 1/2.

Ответ: z = 1/2.