Question

Solve and check
4x-1/3=1/5+3x

CLASS 7​

Answer 1

Answer:

x=8/15

refer the above attachment

Answer 2

★ Solution :-

We have two different methods to solve this equation. The given equation consists of two same variables x. We'll solve both the methods here. The given equation is,

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

The first method is as follows,

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

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

$\sf \leadsto 1x = \dfrac{3 + 5}{15}$

$\sf \leadsto 1x = \dfrac{8}{15}$

$\sf \leadsto x = \dfrac{\dfrac{8}{15}}{1}$

$\sf \leadsto x = \dfrac{8}{15}$

The second method is as follows,

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

$\sf \leadsto \dfrac{12x - 1}{3} = \dfrac{1 + 15x}{5}$

$\sf \leadsto 5(12x - 1) = 3(1 + 15x)$

$\sf \leadsto 60x - 5 = 3 + 45x$

$\sf \leadsto 60x - 45x = 3 + 5$

$\sf \leadsto 15x = 8$

$\sf \leadsto x = \dfrac{8}{15}$

Therefore, the value of x is 8/15.

$\:$

Now, let's check our answer.

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

$\sf \leadsto 4 \bigg( \dfrac{8}{15} \bigg) - \dfrac{1}{3} = \dfrac{1}{5} + 3 \bigg( \dfrac{8}{15} \bigg)$

$\sf \leadsto \dfrac{32}{15} - \dfrac{1}{3} = \dfrac{1}{5} + \dfrac{24}{15}$

$\sf \leadsto \dfrac{32 - 5}{15} = \dfrac{3 + 24}{15}$

$\sf \leadsto \dfrac{27}{15} = \dfrac{27}{15}$

Hence, verified !!