1473. Решите уравнения: 1) 7,2x + 4(2/5)x = 110,2 : 3,8; 2) 3(3/4)x * (1/3 + 0,4) = 1,1; 3) 3,4 * (0,4x + 0,2) + 1,52 = 8,32; 4) 44,62 : (7,8 + 0,5x) + 26,51 = 31,11.

Решение:

1) 7,2x + 4/₅x = 110,2 : 3,8

• \[ 4\frac{2}{5} = 4.4 \]
• \[ 110.2 : 3.8 = 29 \]
• \[ 7.2x + 4.4x = 29 \]
• \[ 11.6x = 29 \]
• \[ x = \frac{29}{11.6} \]
• \[ x = 2.5 \]

2) 3/₄x  (1/3 + 0,4) = 1,1

• \[ 3\frac{3}{4} = 3.75 \]
• \[ \frac{1}{3} + 0.4 = \frac{1}{3} + \frac{4}{10} = \frac{1}{3} + \frac{2}{5} = \frac{5+6}{15} = \frac{11}{15} \]
• \[ 3.75x \times \frac{11}{15} = 1.1 \]
• \[ \frac{15}{4}x \times \frac{11}{15} = 1.1 \]
• \[ \frac{11}{4}x = 1.1 \]
• \[ 2.75x = 1.1 \]
• \[ x = \frac{1.1}{2.75} \]
• \[ x = 0.4 \]

3) 3,4  (0,4x + 0,2) + 1,52 = 8,32

• \[ 3.4(0.4x + 0.2) = 8.32 - 1.52 \]
• \[ 3.4(0.4x + 0.2) = 6.8 \]
• \[ 0.4x + 0.2 = \frac{6.8}{3.4} \]
• \[ 0.4x + 0.2 = 2 \]
• \[ 0.4x = 2 - 0.2 \]
• \[ 0.4x = 1.8 \]
• \[ x = \frac{1.8}{0.4} \]
• \[ x = 4.5 \]

4) 44,62 : (7,8 + 0,5x) + 26,51 = 31,11

• \[ 44.62 : (7.8 + 0.5x) = 31.11 - 26.51 \]
• \[ 44.62 : (7.8 + 0.5x) = 4.6 \]
• \[ 7.8 + 0.5x = \frac{44.62}{4.6} \]
• \[ 7.8 + 0.5x = 9.7 \]
• \[ 0.5x = 9.7 - 7.8 \]
• \[ 0.5x = 1.9 \]
• \[ x = \frac{1.9}{0.5} \]
• \[ x = 3.8 \]

Ответ: 1) x = 2.5; 2) x = 0.4; 3) x = 4.5; 4) x = 3.8.