Question

Решите простые уравнения с модулями 7 класс
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Answer 1

$a)$

$|5 + 8x| = 53 \\ \\ 5 + 8x = 53 \\ 8x = 53 - 5 \\ 8x = 48 \\ x = 6 \\ \\ 5 + 8x = - 53 \\ 8x = - 53 - 5 \\ 8x = - 58 \\ x = - 7.25$

$b)$

$|9x + 8| = 46 \\ \\ 9x + 8 = 46 \\ 9x = 46 - 8 \\ 9x = 38 \\ x = 4 \frac{2}{9} \\ \\ 9x + 8 = - 46 \\ 9x = - 46 - 8 \\ 9x = - 54 \\ x = - 6$

$c)$

$|x + 1| = 3 \\ \\ x + 1 = 3 \\ x = 3 - 1 \\ x = 2 \\ \\ x + 1 = - 3 \\ x = - 3 - 1 \\ x = - 4$

$d)$

$5 |y + 4| = 1.2 \\ |y + 4| = 1.2 \div 5 \\ |y + 4| = 0.24 \\ \\ y + 4 = 0.24 \\ y = 0.24 - 4 \\ y = - 3.76 \\ \\ y + 4 = - 0.24 \\ y = - 0.24 - 4 \\ y = - 4.24$

$e)$

$|9 + 7x| = 30 \\ \\ 9 + 7x = 30 \\ 7x = 30 - 9 \\ 7x = 21 \\ x = 3 \\ \\ 9 + 7x = - 30 \\ 7x = - 30 - 9 \\ 7x = - 39 \\ x = 5 \frac{4}{7}$

$f)$

$|x - 4| = 20 \\ \\ x - 4 = 20 \\ x = 20 + 4 \\ x = 24 \\ \\ x - 4 = - 20 \\ x = - 20 + 4 \\ x = - 16$

$g)$

$|9x - 6| = 3 \\ \\ 9x - 6 = 3 \\ 9x = 3 + 6 \\ 9x = 9 \\ x = 1 \\ \\ 9x - 6 = - 3 \\ 9x = - 3 + 6 \\ 9x = 3 \\ x = \frac{1}{3}$

$h)$

$|3x - 2| = 7 \\ \\ 3x - 2 = 7 \\ 3x = 7 + 2 \\ 3x = 9 \\ x = 3 \\ \\ 3x - 2 = - 7 \\ 3x = - 7 + 2 \\ 3x = - 5 \\ x = - 1 \frac{2}{3}$

$i)$

$|6r - 9| = 27 \\ \\ 6r - 9 = 27 \\ 6r = 27 + 9 \\ 6r = 36 \\ r = 6 \\ \\ 6r - 9 = - 27 \\ 6r = - 27 + 9 \\ 6r = - 18 \\ r = - 3$

$j)$

$|9a - 7| = 70 \\ \\ 9a - 7 = 70 \\ 9a = 70 + 7 \\ 9a = 77 \\ a = 8 \frac{5}{9} \\ \\ 9a - 7 = - 70 \\ 9a = - 70 + 7 \\ 9a = - 63 \\ a = - 7$

$k)$

$|4n + 5| = 19 \\ \\ 4n + 5 = 19 \\ 4n = 19 - 5 \\ 4n = 14 \\ n = 3.5 \\ \\ 4n + 5 = - 19 \\ 4n = - 19 - 5 \\ 4n = - 24 \\ n = - 6$

Answer 2

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