4.315 Найдите корень уравнения и выполните проверку: a) -z⋅5 = -150; в) -0,4у = 44; б) 4⋅(-z) = -32; г) \(\frac{1}{7}\)z = -1; д) \(\frac{5}{7}\)t = \(\frac{25}{28}\); ж) -\(\frac{8}{11}\)t = -1\(\frac{7}{33}\); е) -\(\frac{4}{9}\)z = \(\frac{16}{27}\); з) \(\frac{7}{8}\)z + 7 = 2\(\frac{5}{8}\).

Ответ:

1. a) \[ -z \cdot 5 = -150 \]

   \[ z = \frac{-150}{-5} \]

   \[ z = 30 \]

2. в) \[ -0,4y = 44 \]

   \[ y = \frac{44}{-0,4} \]

   \[ y = -110 \]

3. б) \[ 4 \cdot (-z) = -32 \]

   \[ -z = \frac{-32}{4} \]

   \[ -z = -8 \]

   \[ z = 8 \]

4. г) \(\frac{1}{7}z = -1\)

   \[ z = -1 \cdot 7 \]

   \[ z = -7 \]

5. д) \(\frac{5}{7}t = \frac{25}{28}\)

   \[ t = \frac{25}{28} \cdot \frac{7}{5} \]

   \[ t = \frac{5}{4} \]

6. ж) \[ -\frac{8}{11}t = -1\frac{7}{33} \]

   \[ -\frac{8}{11}t = -\frac{40}{33} \]

   \[ t = -\frac{40}{33} \cdot (-\frac{11}{8}) \]

   \[ t = \frac{5}{3} \]

7. е) \[ -\frac{4}{9}z = \frac{16}{27} \]

   \[ z = \frac{16}{27} \cdot (-\frac{9}{4}) \]

   \[ z = -\frac{4}{3} \]

8. з) \(\frac{7}{8}z + 7 = 2\frac{5}{8}\)

   \[ \frac{7}{8}z + 7 = \frac{21}{8} \]

   \[ \frac{7}{8}z = \frac{21}{8} - 7 \]

   \[ \frac{7}{8}z = \frac{21 - 56}{8} \]

   \[ \frac{7}{8}z = \frac{-35}{8} \]

   \[ z = \frac{-35}{8} \cdot \frac{8}{7} \]

   \[ z = -5 \]

Ответ: