Задание 91

Решение:

• $${\largeа)}\ x=1{,}(0)$$$$\phantom{\largeа)}\ 10x=10{,}(0)$$$$\phantom{\largeа)}\ 10x-x=10-1$$$$\phantom{\largeа)}\ 9x=9$$$$\phantom{\largeа)}\ x=\frac{9}{9}$$$$\phantom{\largeа)}\ x=\frac{1}{1}$$
• $$\phantom{\largeа)}\ x=0{,}(3)$$$$\phantom{\largeа)}\ 10x=3{,}(3)$$$$\phantom{\largeа)}\ 10x-x=3-0$$$$\phantom{\largeа)}\ 9x=3$$$$\phantom{\largeа)}\ x=\frac{3}{9}$$$$\phantom{\largeа)}\ x=\frac{1}{3}$$
• $$\phantom{\largeа)}\ x=0{,}(7)$$$$\phantom{\largeа)}\ 10x=7{,}(7)$$$$\phantom{\largeа)}\ 10x-x=7-0$$$$\phantom{\largeа)}\ 9x=7$$$$\phantom{\largeа)}\ x=\frac{7}{9}$$

• $${\largeб)}\ x=0{,}1(2)$$$$\phantom{\largeб)}\ 10x=1{,}(2)$$$$\phantom{\largeб)}\ 100x=12{,}(2)$$$$\phantom{\largeб)}\ 100x-10x=12-1$$$$\phantom{\largeб)}\ 90x=11$$$$\phantom{\largeб)}\ x=\frac{11}{90}$$
• $$\phantom{\largeб)}\ x=1{,}12(3)$$$$\phantom{\largeб)}\ 100x=112{,}(3)$$$$\phantom{\largeб)}\ 1000x=1123{,}(3)$$$$\phantom{\largeб)}\ 1000x-100x=1123-112$$$$\phantom{\largeб)}\ 900x=1011$$$$\phantom{\largeб)}\ x=\frac{1011}{900}$$$$\phantom{\largeб)}\ x=\frac{337}{300}$$
• $$\phantom{\largeб)}\ x=7{,}5(4)$$$$\phantom{\largeб)}\ 10x=75{,}(4)$$$$\phantom{\largeб)}\ 100x=754{,}(4)$$$$\phantom{\largeб)}\ 100x-10x=754-75$$$$\phantom{\largeб)}\ 90x=679$$$$\phantom{\largeб)}\ x=\frac{679}{90}$$

• $${\largeв)}\ x=0{,}(12)$$$$\phantom{\largeв)}\ 100x=12{,}(12)$$$$\phantom{\largeв)}\ 100x-x=12-0$$$$\phantom{\largeв)}\ 99x=12$$$$\phantom{\largeв)}\ x=\frac{12}{99}$$$$\phantom{\largeв)}\ x=\frac{4}{33}$$
• $$\phantom{\largeв)}\ x=1{,}0(12)$$$$\phantom{\largeв)}\ 10x=10{,}(12)$$$$\phantom{\largeв)}\ 1000x=1012{,}(12)$$$$\phantom{\largeв)}\ 1000x-10x=1012-10$$$$\phantom{\largeв)}\ 990x=1002$$$$\phantom{\largeв)}\ x=\frac{1002}{990}$$$$\phantom{\largeв)}\ x=\frac{167}{165}$$
• $$\phantom{\largeв)}\ x=8{,}7(21)$$$$\phantom{\largeв)}\ 10x=87{,}(21)$$$$\phantom{\largeв)}\ 1000x=8721{,}(21)$$$$\phantom{\largeв)}\ 1000x-10x=8721-87$$$$\phantom{\largeв)}\ 990x=8634$$$$\phantom{\largeв)}\ x=\frac{8634}{990}$$$$\phantom{\largeв)}\ x=\frac{1439}{165}$$

• $${\largeг)}\ x=23{,}5(0)$$$$\phantom{\largeг)}\ 10x=235{,}(0)$$$$\phantom{\largeг)}\ 100x=2350{,}(0)$$$$\phantom{\largeг)}\ 100x-10x=2350-235$$$$\phantom{\largeг)}\ 90x=2115$$$$\phantom{\largeг)}\ x=\frac{2115}{90}$$$$\phantom{\largeг)}\ x=\frac{47}{2}$$
• $$\phantom{\largeг)}\ x=23{,}5(1)$$$$\phantom{\largeг)}\ 10x=235{,}(1)$$$$\phantom{\largeг)}\ 100x=2351{,}(1)$$$$\phantom{\largeг)}\ 100x-10x=2351-235$$$$\phantom{\largeг)}\ 90x=2116$$$$\phantom{\largeг)}\ x=\frac{2116}{90}$$$$\phantom{\largeг)}\ x=\frac{1058}{45}$$
• $$\phantom{\largeг)}\ x=23{,}5(13)$$$$\phantom{\largeг)}\ 10x=235{,}(13)$$$$\phantom{\largeг)}\ 1000x=23\ 513{,}(13)$$$$\phantom{\largeг)}\ 1000x-10x=23\ 513-235$$$$\phantom{\largeг)}\ 990x=23\ 278$$$$\phantom{\largeг)}\ x=\frac{23\ 278}{990}$$$$\phantom{\largeг)}\ x=\frac{11\ 639}{495}$$
• $$\phantom{\largeг)}\ x=23{,}5(127)$$$$\phantom{\largeг)}\ 10x=235{,}(127)$$$$\phantom{\largeг)}\ 10\ 000x=235\ 127{,}(127)$$$$\phantom{\largeг)}\ 10\ 000x-10x=235\ 127-235$$$$\phantom{\largeг)}\ 9990x=234\ 892$$$$\phantom{\largeг)}\ x=\frac{234\ 892}{9990}$$$$\phantom{\largeг)}\ x=\frac{117\ 446}{4995}$$