Question

x/3 - 1/4 =x/5+1/6 . find the value of x.?​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf = > \dfrac{x}{3} - \dfrac{1}{4} = \dfrac{x}{5} + \dfrac{1}{6}$

Now,taking LCM of fractional value to both sides

$\sf = > \dfrac{4x - 3}{12} = \dfrac{6x + 5}{30}$

cross multiply to both sides

➙30(4x-3)=12(6x+5)

➙120x-90= 72x+60

Making like terms together

➙120x-72x= 60+90

➙48x= 150

➙x= 150/48

➙x= 75/24=25/8

Check:

Taking LHS

$\ = > \dfrac{ \dfrac{25}{8} }{3} - \dfrac{1}{4}$

$\sf = > \dfrac{25}{24} - \dfrac{1}{4}$

$\sf = > \dfrac{25 - 6}{24} = \dfrac{19}{24}$

Taking RHS

$\sf = > \dfrac{ \dfrac{25}{8} }{5} + \dfrac{1}{6}$

$\sf = > \dfrac{25}{40} + \dfrac{1}{6}$

$\sf = > \dfrac{75 + 20}{120} = \dfrac{95}{120} = \dfrac{19}{24}$

Hence,LHS = RHS(verified)

Answer 2

Step-by-step explanation:

$\huge\red{Solution}$

$= > \: \frac{x}{3} - \frac{1}{4} = \frac{x}{5} + \frac{1}{6}$

Now, taking LCM of fractional value to both sides

$= > \: \frac{4x - 3}{12} = \frac{6x +5 }{30}$

Multiple to both sides

$= > \: 30(4x - 3) = 12(6x + 5)$

$= > \: 120x - 90 = 72x + 60$

Like terms are...

$= > 120x - 72x = 60 + 90$

$= > 48x = 150$

$= = > x = 150| 48$

$= = > x = 75| 24 = 25| 8$

Taking LHS

$\frac{ \frac{25}{8} }{3} - \frac{1}{4}$

$\frac{25}{24} - \frac{1}{4}$

$= = > \: \frac{25 - 6}{24} = \frac{19}{24}$

Taking RHS

$= = > \: \frac{ \frac{25}{8} }{5} + \frac{1}{6}$

$= = > \: \frac{25}{40} + \frac{1}{6}$

$= = > \: \frac{75 + 20}{120} = \frac{95}{120} = \frac{19}{24}$

✍ Hope it's helpful to you ✍