Question

A terça parte do valor da raiz da equação 0,666...(2t+3)-0,75(t+1)=1

Answer 1

  A terça parte do valor da raiz da equação 0,666...(2t+3)-0,75(t+1)=1

IDENTIFICANDO
A terça parte = 1/3
0,75 = 75/100
0,666 = 6/9
para saber

     x   =  0,666  (10) multiplica
10x   =   6,666 (subtrai)
--------------------------------
  9x  =   6,00000
9x = 6
x = 6/9

0,666...(2t+3)-0,75(t+1)=1
      6/9 (2t + 3) - 75/100(t+1) = 1

      6                     75
--------(2t + 3)   -  -------(t+1) = 1
      9                    100

   
       6(2t + 3)         75(t + 1)
    ---------------- -  --------------  = 1                    mmc 9,100| 2
           9                     100                                         9, 50| 2
                                                                                 9, 25| 3 
      12t + 18           75t + 75                                      3, 25 | 3
     --------------- - ----------------- = 1                             1, 25| 5
           9                   100                                            1,  5| 5
                                                                                   1,1/  = 2.2.3.3.5.5 =
                                                                                           = 4.9.25 = 900

     100(12t + 18) - 9(75t + 75) = 1(900)
---------------------------------------------------- FRAÇÃO com igualdade desprezamos
                          900                               0 denominador

100(12t + 18) - 9(75t + 75) = 1(900)
1200t + 1800 - 675t -675   = 900
1200t - 675t + 1800 - 675 = 900
  525t + 1125 = 900
525t = 900 - 1125
525t = - 225
t = -  225/525
          225 : 75        3
t = -  ----------   =  - ------
          525  : 75       7

t = - 3/7

1/3 de - 3/7

  1           3
-----  de - -----
  3           7

1 x (-3/7) : 3 =
-  3/7 : 3

    3        1             3                3: 3              1
-  -----x ----- = -  ------   e    -  ----------  =  - -------
     7       3            21             21: 3              7