Question

2.
What is the value of x in the given equation?
(3x + 1)/16+(2x-3)/7=(x+3)/8+(3x-1)/14​

Answer 1

Answer:

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

Step-by-step explanation:

By taking LCM for 16, 7, 8 and 14 which is 112 :-

((3x+1)7 + (2x-3)16 – (x+3)14 – (3x-1)8)/112 = 0 (21x + 7 + 32x – 48 – 14x – 42 – 24x + 8)/112 = 0 (21x + 32x – 14x – 24x + 7 – 48 – 42 + 8)/112 = 0 (15x – 75)/112 = 0

By cross-multiplying

15x – 75 = 0

15x = 75

x = 75/15

= 5

Let us verify the given equation now,

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

By substituting the value of ‘x’ we get,

(3(5)+1)/16 + (2(5)-3)/7 = (5+3)/8 + (3(5)-1)/14

(15+1)/16 + (10-3)/7 = 8/8 + (15-1)/14

16/16 + 7/7 = 8/8 + 14/14

16/16 + 7/7 = 8/8 + 14/14

1 + 1 = 1 + 1

2 = 2