Упр.32.16 Часть 2 ГДЗ Мордкович Семенов 7 класс (Алгебра)

а) (3x — 5) — (x + 7) = 12x — 17;
б) (-1/3 x — 0,4) — (5/6 x — 0,3) = -(x + 1);
в) -(1 — 4x) + (6x — 11) = 24 — 2x;
г) (0,04x + 4/9) — (2/3 + 0,4x) = -2 — x.

1. а) $$ (3x — 5) — (x + 7) = 12x — 17 $$

   $$ 3x — 5 — x — 7 = 12x — 17 $$

   $$ 2x — 12 = 12x — 17 $$

   $$ 2x — 12x = -17 + 12 $$

   $$ -10x = -5 $$

   $$ x = 0{,}5 $$

2. б) $$ \left(-\frac{1}{3}x — 0{,}4\right) — \left(\frac{5}{6}x — 0{,}3\right) = -(x + 1) $$

   $$ -\frac{1}{3}x — 0{,}4 — \frac{5}{6}x + 0{,}3 = -x — 1 $$

   $$ -\frac{2}{6}x — \frac{5}{6}x — 0{,}1 = -x — 1 $$

   $$ -\frac{7}{6}x — 0{,}1 = -x — 1 $$

   $$ -\frac{7}{6}x + x = -1 + 0{,}1 $$

   $$ -\frac{1}{6}x = -0{,}9 $$

   $$ x = 5{,}4 $$

3. в) $$ -(1 — 4x) + (6x — 11) = 24 — 2x $$

   $$ -1 + 4x + 6x — 11 = 24 — 2x $$

   $$ 10x — 12 = 24 — 2x $$

   $$ 10x + 2x = 24 + 12 $$

   $$ 12x = 36 $$

   $$ x = 3 $$

4. г) $$ \left(0{,}04x + \frac{4}{9}\right) — \left(\frac{2}{3} + 0{,}4x\right) = -2 — x $$

   $$ 0{,}04x + \frac{4}{9} — \frac{2}{3} — 0{,}4x = -2 — x $$

   $$ -0{,}36x + \frac{4}{9} — \frac{6}{9} = -2 — x $$

   $$ -0{,}36x — \frac{2}{9} = -2 — x $$

   $$ -0{,}36x + x = -2 + \frac{2}{9} $$

   $$ 0{,}64x = -\frac{16}{9} $$

   $$ x = -\frac{16}{9} \cdot \frac{100}{64} = -\frac{25}{9} $$

Ответ

а) $$x = 0{,}5$$; б) $$x = 5{,}4$$; в) $$x = 3$$; г) $$x = -\frac{25}{9}$$.