Solve the equation:\(\frac{x+2}{2} + \frac{x+4}{3} = \frac{x +6}{4} +

1.	Solve the equation:\(\frac{x+2}{2} + \frac{x+4}{3} = \frac{x +6}{4} + \frac{x +8}{5}\)
Answer» \(\frac{x+2}{2} + \frac{x+4}{3} = \frac{x +6}{4} + \frac{x +8}{5}\) ⇒ 30(x + 2) + 20(x + 4) = 15(x + 6) + 12(x + 8) On multiplying by LCM of 2, 3, 4 and 5 i.e. 60 on both sides ⇒ 30x + 60 + 20x + 80 = 15x + 90 + 12x + 96 ⇒ 30x + 20x + 60 + 80 = 15x + 12x + 90 + 96 ⇒ 50x + 140 = 27x + 186 ⇒ 50x – 27x = 186 – 140 On transposing 140 and 27x ⇒ 23x = 46 ⇒ 23x/23 = 46/23 On dividing by 23 on both sides ⇒ x = 2

Solve the equation:\(\frac{x+2}{2} + \frac{x+4}{3} = \frac{x +6}{4} + \frac{x +8}{5}\)

Answer»

\(\frac{x+2}{2} + \frac{x+4}{3} = \frac{x +6}{4} + \frac{x +8}{5}\)

⇒ 30(x + 2) + 20(x + 4) = 15(x + 6) + 12(x + 8)

On multiplying by LCM of 2, 3, 4 and 5 i.e. 60 on both sides

⇒ 30x + 60 + 20x + 80 = 15x + 90 + 12x + 96

⇒ 30x + 20x + 60 + 80 = 15x + 12x + 90 + 96

⇒ 50x + 140 = 27x + 186

⇒ 50x – 27x = 186 – 140

On transposing 140 and 27x

⇒ 23x = 46

⇒ 23x/23 = 46/23

On dividing by 23 on both sides

⇒ x = 2