Equations5 and 6

In this page solution of equations5 and 6 we are going to see solution for fifth and sixth questions.

Question 5:

Solve the equation (2 x - 7)/5 - (x - 4)/3 = (x - 4)/6

Solution:

           (2 x - 7)/5 - (x - 4)/3 = (x - 4)/6 

           3(2 x - 7)/(5 x 3) - 5(x - 4)/(3 x 5) = (x - 4)/6

           (6 x - 21)/15 - (5 x - 20)/15 = (x - 4)/6

           [(6 x - 21) - (5 x - 20)]/15 = (x - 4)/6

           (6 x - 21 - 5 x + 20)/15 = (x - 4)/6

            (6 x - 5x - 21 + 20)/15 = (x - 4)/6

                (x - 1)/15 = (x - 4)/6

                6 (x - 1) = 15 (x - 4)

                 6 x - 6 = 15 x - 60

                 6 x - 15 x = - 60 + 6

                      - 9 x = - 54

                           x =  -54/(-9)

                           x = 6

Checking:

 

(2 x - 7)/5 - (x - 4)/3 = (x - 4)/6

 (2(6)-7)/5 - (6 - 4)/3  = (6- 4)/6

 (12-7)/5 - 2/3  = 2/6

 5/5 - 2/3  =1/3

 1 - (2/3) = 1/3

 (3 - 2)/3 = 1/3

    1/3 = 1/3

 

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Question 6:

Solve the equation (5 x - 7)/4 - ( 8x - 4)/5 = (2 x - 3)/10

Solution:

           ( 5 x - 7)/4 - ( 8x - 4)/5 = (2 x - 3)/10 

           5(5 x - 7)/(4 x 5) - 4(8x - 4)/(5 x 4) = (2 x - 3)/10 

           (25 x - 35)/20 - (32 x - 16)/20 = (2 x - 3)/10

           (25 x - 35) - (32 x - 16) /20 = (2 x - 3)/10

           (25 x - 35 - 32 x + 16)/20 = (2 x - 3)/10

           (25 x - 32 x - 35 + 16)/20 = (2 x - 3)/10

                     (- 7x - 19)/20 = (2x - 3)/10

                       10 (-7 x - 19) = 20 (2 x - 3)

                         - 70 x - 190 = 40 x - 60

                           - 70 x - 40 x = - 60 + 190

                             - 110 x = 130

                                     x = 130/(-110)

                                     x = -13/11

Checking:

 

(5 x - 7)/4 - ( 8x - 4)/5 = (2 x - 3)/10

 (5(-13/11)-7)/4 - (8(-13/11) - 4)/5  = (2(-13/11)-3)/10

 [(-65/11 )-7]/4 - [(-104/11)-4]/5  = [(-26/11 ) - 3]/10

[-65-7(11)]/(11x4)-[-104- 4(11)/(11x5)=[-26-3(11)]/(11 x 10)

[(-65 - 77)/44] - [(- 104 - 44)/55]  = (-26 - 33)/110

(- 142/44) - (-148/55) = -59/110

 (-142 x 55)/(44 x 55) - (-148 x 44)/(55 x 44) = - 59/110

(-7810/2420) - (-6512/2420) = - 59/110

 (-7810 + 6512)/2420 = -59/110

 -1298/2420 = -59/110

 0.5363...= 0.5363......

Those are the solution of equations5 and 6

equations5 and 6 to Worksheet