Question

116. Найдите корень уравнения: 1) (63 – 5x) :a= 6 при а = 3; 2) b: (38х - 95) = 7 при b = 133; 3) 15 : (с – 8x) = 75 при с= 53; ; 4) (6x - d) - 8 = 104 при d = 29. .​

Answer 1

1)

$(63 - 5x) \div a = 6$

$63 - 5x = 6a$

$- 5x = 6a - 63$

$x = - \frac{6a - 63}{5}$

при $a = 3$,

$x = - \frac{6 \times 3 - 63}{5} = - \frac{18 - 63}{5} = - \frac{ - 45}{5} = \frac{45}{5} = 9$

2)

$b \div (38x - 95) = 7$

$38x - 95 = b \div 7$

$38x = \frac{b}{7} + 95$

$38x = \frac{b + 665}{7}$

$x = \frac{b + 665}{7} \div 38$

$x = \frac{b + 665}{266}$

при $b = 133$,

$x = \frac{133 + 665}{266} = \frac{798}{266} = 3$

3)

$15 \div (c - 8x) = 75$

$c - 8x = 15 \div 75$

$c - 8x = \frac{1}{5}$

$- 8x = \frac{1}{5} - c$

$- 8x = \frac{1 - 5c}{5}$

$x = \frac{1 - 5c}{5} \div ( - 8)$

$x = - \frac{1 - 5c}{40}$

при $c = 53$,

$x = - \frac{1 - 5 \times 53}{40} = - \frac{1 - 265}{40} = - \frac{ - 264}{40} = \frac{264}{40} = \frac{66}{10} = 6.6$

4)

$(6x - d) - 8 = 104$

$6x - d = 104 + 8$

$6x - d = 112$

$6x = 112 + d$

$x = \frac{112 + d}{6}$

при $d = 29$,

$x = \frac{112 + 29}{6} = \frac{141}{6} = \frac{47}{2} = 23.5$