Equations3 and 4

In this page equations3 and 4 we are going to see solution for third and fourth questions.

Question 3:

Solve the equation ( 2 x - 7 )/5 + ( x + 9 )/15 = ( 2 x - 2 )/5

Solution:

           ( 2 x - 7 )/5 + ( x + 9 )/15 = ( 2 x - 2 )/5

Taking L.C.M

           3 ( 2 x - 7 )/(5 x 3) + ( x + 9 )/15 = ( 2 x - 2 )/5

           3 ( 2 x - 7)/15 + ( x + 9 )/15 = (2 x - 2)/5   

           (6 x - 21)/15 + ( x + 9 )/15 = ( 2x - 2)/5

            ( 6 x - 21 + x + 9 )/15  = ( 2 x - 2 )/ 5

             ( 6 x + x - 21 + 9 )/15 = ( 2 x - 2 )/5

                ( 7 x - 12)/15 = ( 2x - 2 )/5

                 5 ( 7 x - 12 ) = 15 ( 2x - 2)

                    35 x - 60 = 30 x - 30

                 35 x - 30 x = - 30 + 60

                           5 x = 30

                             x = 30/5

                             x = 6

Checking:

 ( 2 (6) - 7 )/5 + ( 6 + 9 )/15 = ( 2 (6) - 2 )/5 

  ( 12 - 7 )/5  +  15/15  = (12 - 2)/5

  ( 5 /5 ) + 1 = 10/5

    1 + 1 = 2

           2 = 2

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Question 4:

Solve the equation ( 3 x + 41 )/2 + ( x - 3 )/5 = ( 9 - 2 x )/6

Solution:

           (3 x + 41)/2 + (X - 3)/5 = (9 - 2 x)/6

Taking L.C.M 

            (3 x + 41)/2 + (X - 3)/5 = (9 - 2 x)/6

            5 (3 x + 41)/(2 x 5) + 2 (x - 3)/(5 x 2)  = (9 - 2 x)/6

            (15 x + 205)/10 + (2 x - 6)/10 = (9 - 2 x)/6

             (15 x + 205 + 2 x - 6)/10 = (9 - 2 x)/6

              (15 x + 2 x + 205 - 6) /10 = (9 - 2x)/6

               (17 x + 199)/10 = (9 - 2 x)/6  

                6 (17 x + 199) = 10 (9 - 2 x)

                102 x + 1194 = 90 - 20 x

                102 x + 20 x = 90 - 1194

                         122 x = -1104

                               x = -1104/122

                               x = -552/61

Checking:

( 3 x + 41 )/2 + ( x - 3 )/5 = ( 9 - 2 x )/6 

[3 (-552/61) + 41]/2 + [(-552/61)  - 3 )]/5 = [9 - 2(-552/61)]/6

 [(-1656/61)  + 41]/2  + [(-552 - 3(61))/61]/5   = [(9+1104/61)]/6

(-1656+41(61)/(2 x 61)+(-552-183)/(61x5)=(9(61)+1104)/(61x6)

(-1656 + 2501)/122 + (-735/305) = (549+1104)/366

( 845/122) + (-735/305) = 1653/366

 (845 x 305)/(122x 305) + (-735x122)/(305x122) = 1653/366

(257725/37210) + (-89670/37210) = 1653/366

(257725 - 89670)/37210 = 1653/366

168055/37210 = 1653/366

4.51 = 4.51

equations3 and 4

Equations3 and 4 to Worksheet