Exercícios de equação do 1º grau resolvidos

1) Resolva as equações abaixo:

a) 2x - 6 = - x + 15                                       b) 2(x - 3) - 4x = - 3x - 8 

2x + x = 15 + 6                                                 2x - 6 - 4x = - 3x - 8   

3x = 21                                                             2x - 4x + 3x = - 8 + 6

x = 21/3                                                                  x = - 2 

x = 7                                                                      x = - 2

S = {7}                                                                    S = {-2}

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c) 8x - (x + 3) = 11                                       d) 100x + 80 = 120x - (40x - 300)

  8x - x - 3 = 11                                                 100x + 80 = 120x -40x + 300

  8x - x = 11 + 3                                                   100x - 120x + 40x = 300 - 80

     7x = 14                                                             140x -120x = 220

    x = 14/7                                                                 20x = 220

    x = 14/7                                                                     x = 220/20

 x = 2  → S = [2}                                                               x = 11

                                                                                      S = {11}

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.

e) 9 - 3(2x - 8) + 2(4 - 5x) = 20 - (5 + 2x)       f) 50x + 200 = 20(x - 4) + 100         

9 - 6x + 24 + 8 -10x = 20 - 5 - 2x                      50x + 200 = 20x - 80 + 100

-6x - 10x + 2x = 20 - 5 - 9 -  24 - 8                       50x - 20x = - 80 + 100 -200

- 16x + 2x = 20 - 46                                                30x = -280 + 100

- 14x = - 26    . (-1)                                                    30x = - 180

14x = 26                                                                    x = -180/30

x = 26/14                                                                       x = - 6

x = 13/7   → S = {13/7}                                                S = {- 6}

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g) 14t - 9 - 3t = 2t + 36                                  h) 6m + 3(10 - 4m) = 25 + 8m

      14t - 3t - 2t =  36 + 9                                    6m + 30 - 12m = 25 + 8m

          14t - 5t = 45                                              6m - 12m - 8m = 25 - 30

             9t = 45                                                       6m - 20m = - 5

                 t = 45/9                                                      - 14m = -5

                  t = 5                                                            14m = 5

                   S = {5}                                                 m = 5/14 → S = {5/14}

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 2) Resolva as equações abaixo em R.

       3x      x - 10          x + 1 

a)   ——— - ——— =  ————  

        2         8              4              

 .

        8(3x)  2(x - 10)   4(x + 1)  

      ——— - ——— =  ———— 

        16        16            16   

 .

        8(3x)  -2(x - 10)  = 4(x + 1) 

   .                                            

           24x   - 2x + 20=  4x + 4 

.

              24x - 2x - 4x = 4- 20

.              

                     18x = - 16

.

                     x = - 16/18

.

                       x = - 8/ 9

 .

                         S = {-8/9}

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      x + 6     2x - 3       x - 1 

b)   ——— - ——— =  ————  

        3          6             4              

 .

       4(x + 6)      2(2x - 3)      3(x - 1)  

      ————— - ————— =  ———— 

           12            12               12  

 .

     4(x + 6)  - 2(2x - 3)  =  3(x - 1)       

   .                                            

        4x + 24 - 4x + 6 = 3x - 3

.

        4x - 4x - 3x = - 3 - 24 - 6

.              

                 - 3x = - 33

.

                   3x =  33

.

                    x = 33/3

   .                     

                     x = 11

 .

                 S = {11}