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D Divya Prakash Singh
We have                             Transposing 5m to the LHS                             or                            Dividing both sides by -2, we get                                   Check :- Put      in the LHS and the RHS:                LHS :-                                                    RHS :-                                      Hence,      LHS = RHS

D Divya Prakash Singh
We have                                      Transposing      to the LHS and 1 to the RHS:                                  or                                or                                         or                                        x = 10 Check  :- Put x = 10 in both the LHS and the RHS                 LHS :                                                   RHS :                    ...

D Divya Prakash Singh
We have                            8x + 4 = 3 (x - 1) + 7 or                       8x + 4 = 3x - 3 + 7 = 3x + 4 Transposing 3x to the LHS and 4 to the RHS, we get                          8x - 3x = 4 - 4 = 0                             5x = 0 Dividing both sides by 5:                          x = 0  Check :-   Putting x = 0 in both LHS and RHS:                LHS :- 8x + 4 = 8(0) + 4 = 4      ...

D Divya Prakash Singh
We have                         2x - 1 = 14 - x Transposing -x to the LHS and -1 to the RHS                        2x + x = 14 + 1 or                        3x = 15  Dividing both sides by 3, we get                         x = 5  Check :-  Put x = 5 in both the LHS and the RHS                  LHS :-     2x - 1 = 2(5) - 1 = 10 - 1 = 9                  RHS :-     14 - x = 14 - 5 = 9 Hence,     ...

5x-3x+9=5

2x+9=5

2x=5-9

2x=-4

x= -2

hence the value of x is -2

D Divya Prakash Singh
We have              5t - 3 = 3t - 5 Transposing 3t to the LHS and -3 to the RHS, we get:            5t - 3t = -5 + 3 or            2t = -2 Dividing both sides by 2 :              t = -1 Check:-             Put t = -1 in the LHS we have,                              5t - 3 = 5(-1) - 3 = -5 -3 = -8                          Similarly put t = -1 in the RHS:                              3t - 5 =...

D Divya Prakash Singh
At first, transposing 17 to the RHS:   6p = 9 - 17 = -8 Now, dividing both sides by 6, we get

D Divya Prakash Singh
Transposing -8 to the RHS, we get   14y = 13 + 8 = 21 Now dividing both sides by 14:

D Divya Prakash Singh
Transposing 9 to the RHS, we get  7x = 16 + 9 = 25 Now, dividing both sides by :

D Divya Prakash Singh
Multiplying both sides by 1.5, we get  Thus y = 2.4

D Divya Prakash Singh
Multiplying both sides by 5, we get  Thus t = 50

D Divya Prakash Singh
Dividing both sides by 6, we get    Thus   x = 2

D Divya Prakash Singh
Transposing 2 to the LHS, we get       6 - 2 = z => z= 4    Thus   z = 4

D Divya Prakash Singh
Transposing 3 to the RHS, we get   y = 10 - 3 = 7   y = 7

D Divya Prakash Singh
Let the numerator of the rational number be x. Then denominator will be x + 8. Further, according to question,                       or                      Cross-multiplication gives:                          2(x + 17)  =  3(x + 7) or                   2x + 34  =  3x + 21 or                        x  = 13 Hence the rational number is   .

D Divya Prakash Singh
Let the present ages of Hari and Harry be 5x and 7x respectively. (Since there are in the ratio of 5:7) Four years from age of Hari will be = 5x + 4 and Harry's age will be = 7x + 4. According to question four years from now, the ratio of their ages will be 3:4. So the equation becomes :                                                   Cross-multiplication gives:                              ...

D Divya Prakash Singh
We have                        Cross-multiplication gives,                    3(7y + 4)  =  -4(y + 2) or             21y + 12  =  -4y - 8 or              21y + 4y = -8 - 12 or                    25y  =  -20

D Divya Prakash Singh
We have                           Cross-multiplication gives:                       9z = 4z + 60 or           9z - 4z  = 60 or                  5z = 60  or                    z = 12