4x/9 + 1/3 + 13x/108 = (8x+19)/18
Let us rearrange the equation
4x/9 + 13x/108 – (8x+19)/18 = -1/3
By taking LCM for 9, 108 and 18 which is 108
((4x×12) + 13x×1 – (8x+19)6)/108 = -1/3
(48x + 13x – 48x – 114)/108 = -1/3
(13x – 114)/108 = -1/3
By cross-multiplying
(13x – 114)3 = -108
39x – 342 = -108
39x = -108 + 342
39x = 234
x = 234/39
= 6
Let us verify the given equation now,
4x/9 + 1/3 + 13x/108 = (8x+19)/18
By substituting the value of ‘x’ we get,
4(6)/9 + 1/3 + 13(6)/108 = (8(6)+19)/18
24/9 + 1/3 + 78/108 = 67/18
8/3 + 1/3 + 13/18 = 67/18
((8×6) + (1×6) + (13×1))/18 = 67/18
(48 + 6 + 13)/18 = 67/18
67/18 = 67/18
Hence, the given equation is verified.
