Question

(3x+1)/16+(2x-3)/7=(x+3)/8+(3x-1)/14

Answer 1

( 3 x + 1 ) / 16 + ( 2 x - 3 ) / 7 = ( x + 3 ) / 8 + ( 3 x - 1 ) / 14
 21 x + 7 + 32 x - 48 / 112  =  7 x + 21 + 12 x - 4 / 56
 53 x - 41 / 112 = 19 x + 17 / 56      [ (112 : 56)  = ( 2:1 )  ]
 53 x - 41 = 38 x + 34
 53 x-38 x = 34 + 41
 15 x = 75
 x = 75/15
 x = 5

Answer 2

Given,

(3x+1)/16+(2x-3)/7 = (x+3)/8+(3x-1)/14

To find,

The value of x.

Solution,

The value of x after solving the equation will be 5.

We can easily solve this problem by following the given steps.

According to the question,

(3x+1)/16+(2x-3)/7=(x+3)/8+(3x-1)/14

Taking the LCM of the denominators using the prime factorization method and adding the fractions,

7(3x+1)+16(2x-3)/112 = 7(x+3)+4(3x-1)/56

( Note that the fractions are added when the denominator divides the LCM and the quotient is multiplied by the numerator.)

21x+7+32x-48/112 = 7x+21+12x-4/56

53x-41/112 = 19x+17/56

Dividing 112 by 56,

53x-41/2 = 19x+17

Using the cross multiplication method,

(53x-41) = 2(19x+17)

53x-41 = 38x+34

53x-38x-41 = 34 (Moving 38x from the right-hand side to the left-hand side will result in the change of sign from plus to minus.)

15x-41 = 34

15x = 34+41 ( Moving 41 from the left-hand side to the right-hand side will result in the change of sign from minus to plus.)

15x = 75

x = 75/15

x = 5

Hence, the value of x is 5.