5.218 Найдите корень уравнения: a) \frac{x-11}{15} = 16; б) \frac{54}{y+7} = 6; в) \frac{m+6}{11} = 4; г) \frac{108}{20- c} = 9.

1. a) $$\frac{x-11}{15} = 16$$

   $$x - 11 = 16 \cdot 15$$

        16
       x15
       ---
        80
    +16
    ----
       240
       

   $$x - 11 = 240$$

   $$x = 240 + 11$$

   $$x = 251$$

2. б) $$\frac{54}{y+7} = 6$$

   $$y + 7 = \frac{54}{6}$$

   $$y + 7 = 9$$

   $$y = 9 - 7$$

   $$y = 2$$

3. в) $$\frac{m+6}{11} = 4$$

   $$m + 6 = 4 \cdot 11$$

   $$m + 6 = 44$$

   $$m = 44 - 6$$

   $$m = 38$$

4. г) $$\frac{108}{20- c} = 9$$

   $$20 - c = \frac{108}{9}$$

   $$20 - c = 12$$

   $$c = 20 - 12$$

   $$c = 8$$

Ответ: a) $$x=251$$, б) $$y=2$$, в) $$m=38$$, г) $$c=8$$