298. Решите уравнения: a) 5y + 27 = 4y + 21; б) 7m - 11 = 10m + 16; в) 5,6 + 0,6х = 0,3x - 1,3; г) 0,37х - 8,92 = 0,38x - 3,59; д) 2 1/3 x + 2 5/12 = 3 2/9 x + 1 1/4; e) 3/7 x - 1/4 x = 5 3/7 - 4x.

Решение:

1. а) \( 5y + 27 = 4y + 21 \)
   \( 5y - 4y = 21 - 27 \)
   \( y = -6 \)


2. б) \( 7m - 11 = 10m + 16 \)
   \( 7m - 10m = 16 + 11 \)
   \( -3m = 27 \)
   \( m = -9 \)


3. в) \( 5,6 + 0,6x = 0,3x - 1,3 \)
   \( 0,6x - 0,3x = -1,3 - 5,6 \)
   \( 0,3x = -6,9 \)
   \( x = -23 \)


4. г) \( 0,37x - 8,92 = 0,38x - 3,59 \)
   \( 0,37x - 0,38x = -3,59 + 8,92 \)
   \( -0,01x = 5,33 \)
   \( x = -533 \)


5. д) \( 2\frac{1}{3}x + 2\frac{5}{12} = 3\frac{2}{9}x + 1\frac{1}{4} \)
   \( \frac{7}{3}x + \frac{29}{12} = \frac{29}{9}x + \frac{5}{4} \)
   \( \frac{29}{12} - \frac{5}{4} = \frac{29}{9}x - \frac{7}{3}x \)
   \( \frac{29 - 15}{12} = \frac{29 - 21}{9}x \)
   \( \frac{14}{12} = \frac{8}{9}x \)
   \( \frac{7}{6} = \frac{8}{9}x \)
   \( x = \frac{7}{6} \cdot \frac{9}{8} = \frac{63}{48} = \frac{21}{16} \)


6. е) \( \frac{3}{7}x - \frac{1}{4}x = 5\frac{3}{7} - 4x \)
   \( \frac{3}{7}x - \frac{1}{4}x + 4x = \frac{38}{7} \)
   \( (\frac{12 - 7 + 112}{28})x = \frac{38}{7} \)
   \( \frac{117}{28}x = \frac{38}{7} \)
   \( x = \frac{38}{7} \cdot \frac{28}{117} = \frac{38 \cdot 4}{117} = \frac{152}{117} \)

Ответ: а) -6; б) -9; в) -23; г) -533; д) \(\frac{21}{16}\); е) \(\frac{152}{117}\).