Розв'яжіть рівняння (409-410). 409.a) 4x-5-(7x + 8) = 2; 6) 9z + 17 - (4z - 5) = 38; B) 24-(x² + 8x-17) = 5 - 5x - x²; r) 19-(3x²-2x) - (6x-x²) =7-2x².

Решение

а) $$4x - 5 - (7x + 8) = 2$$

$$4x - 5 - 7x - 8 = 2$$

$$-3x - 13 = 2$$

$$-3x = 2 + 13$$

$$-3x = 15$$

$$x = \frac{15}{-3}$$

$$x = -5$$

б) $$9z + 17 - (4z - 5) = 38$$

$$9z + 17 - 4z + 5 = 38$$

$$5z + 22 = 38$$

$$5z = 38 - 22$$

$$5z = 16$$

$$z = \frac{16}{5}$$

$$z = 3.2$$

в) $$24 - (x^2 + 8x - 17) = 5 - 5x - x^2$$

$$24 - x^2 - 8x + 17 = 5 - 5x - x^2$$

$$41 - x^2 - 8x = 5 - 5x - x^2$$

$$41 - 8x = 5 - 5x$$

$$41 - 5 = -5x + 8x$$

$$36 = 3x$$

$$x = \frac{36}{3}$$

$$x = 12$$

г) $$19 - (3x^2 - 2x) - (6x - x^2) = 7 - 2x^2$$

$$19 - 3x^2 + 2x - 6x + x^2 = 7 - 2x^2$$

$$19 - 2x^2 - 4x = 7 - 2x^2$$

$$19 - 4x = 7$$

$$19 - 7 = 4x$$

$$12 = 4x$$

$$x = \frac{12}{4}$$

$$x = 3$$

Ответ: а) $$x = -5$$; б) $$z = 3.2$$; в) $$x = 12$$; г) $$x = 3$$.