52. Решите уравнение: a) 22x + x - 10 = 59; б) 14y - 2y + 76 = 100; в) (7а - 2а) · 8 = 80; г) (15b + b) : 4 = 3; д) (0,87m – 0,66m) · 10 : 2 : 3 = 0; e) 10 · (1,37k - 0,12k) : 5 : 8 = 0.

Решение:

• a) \( 22x + x - 10 = 59 \\ 23x = 69 \\ x = \frac{69}{23} \\ x = 3 \)
• б) \( 14y - 2y + 76 = 100 \\ 12y = 100 - 76 \\ 12y = 24 \\ y = \frac{24}{12} \\ y = 2 \)
• в) \( (7a - 2a) \cdot 8 = 80 \\ 5a \cdot 8 = 80 \\ 40a = 80 \\ a = \frac{80}{40} \\ a = 2 \)
• г) \( (15b + b) \div 4 = 3 \\ 16b \div 4 = 3 \\ 4b = 3 \\ b = \frac{3}{4} \\ b = 0.75 \)
• д) \( (0.87m - 0.66m) \cdot 10 \div 2 \div 3 = 0 \\ 0.21m \cdot 10 \div 2 \div 3 = 0 \\ 2.1m \div 2 \div 3 = 0 \\ 1.05m \div 3 = 0 \\ 0.35m = 0 \\ m = 0 \)
• e) \( 10 \cdot (1.37k - 0.12k) \div 5 \div 8 = 0 \\ 10 \cdot (1.25k) \div 5 \div 8 = 0 \\ 12.5k \div 5 \div 8 = 0 \\ 2.5k \div 8 = 0 \\ 0.3125k = 0 \\ k = 0 \)

Ответ: a) x = 3, б) y = 2, в) a = 2, г) b = 0.75, д) m = 0, e) k = 0