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Solve the following equation and check your result. 

Q.10           

               3m = 5m - \frac{8}{5}

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

Solve the following equation and check your result.

Q.8 

                 \frac{2x}{3}+1 = \frac{7x}{15}+3

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 :                    ...

Solve the following equation and check your result.

Q.6  8x + 4 = 3 (x – 1) + 7

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      ...

Solve the following equation and check your result.

Q.5    2x – 1 = 14 – x

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,     ...

Solve the following equation and check your result.

Q.3     5x + 9 = 5 + 3x

We have                       5x + 9 = 5 + 3x     Transposing 3x to the LHS and 9 to the RHS, we get:                      5x - 3x = 5 - 9 or                      2x = -4 Dividing both sides by 2 :                    x = -2 Check :-    Put x = - 2 in both LHS and RHS                LHS :-  5x + 9 = 5(-2) + 9 =  -10 + 9 = -1                RHS :-  5 + 3x = 5 + 3(-2) = 5 - 6 = -1          ...

Solve the following equation and check your result.

Q.2    5t – 3 = 3t – 5

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 =...

Solve the following equation.

Q.11    17 + 6p = 9

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

Solve the following equation.

Q.10    14y – 8 = 13

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

Solve the following equation.

Q.9   7x – 9 = 16

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

Solve the following equation.

Q.8        1.6 = \frac{y}{1.5}

Multiplying both sides by 1.5, we get  Thus y = 2.4

Solve the following equation.

Q.6      \frac{t}{5} = 10

Multiplying both sides by 5, we get  Thus t = 50

Solve the following equation.

Q.5    6x = 12

Dividing both sides by 6, we get    Thus   x = 2

Solve the following equation.

Q.3   6 = z + 2

Transposing 2 to the LHS, we get       6 - 2 = z => z= 4    Thus   z = 4 

Solve the following equation.

Q.2 .  y + 3 = 10

Transposing 3 to the RHS, we get   y = 10 - 3 = 7   y = 7

Q.7 The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.

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   .

Q.6  The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.

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:                              ...

Solve the following equation.

Q.5 

            \frac{7y+4}{y+2} = \frac{-4}{3}

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

Solve the following equation.

Q.3

        \frac{z}{z+15} = \frac{4}{9}

 

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

Solve the following equation.

Q4.

         \frac{3y+4}{2-6y} = \frac{-2}{5}

We have                By cross-multiplication we get:                 5(3y + 4)   =  -2(2 - 6y) or             15y + 20 = -4 + 12y or              15y - 12y = -4 - 20 or                    3y = -24                         y = -8

Solve the following equation.

Q.2   

                \frac{9x}{7-6x} = 15

We will convert the given equation into a linear equation by multiplying   (7 - 6x) to both sides. Equation becomes:   9x = 15(7 - 6x) or                               9x = 105 - 90x or                              99x = 105                          
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