Question

Solve equation and check the answer x+2/3=3x-2/5

Answer 1

Here is the answer

$\tt {x + \frac{2}{3} = 3x - \frac{2}{5}}$

$\bf { \frac{2}{3} = 3x - x - \frac{2}{5} }$

$\bf{ \frac{2}{3} = 2x - \frac{2}{5} }$

$\bf{ \frac{2}{3} + \frac{2}{5} = 2x }$

Equal the Denominator

$\bf{\frac{2 \times 5}{3 \times 5} + \frac{2 \times 3}{5 \times 3} = 2x}$

$\bf{\frac{10}{15} + \frac{6}{15} = 2x}$
$\bf {\frac{16}{15} = 2x}$

$\bf {\frac{ \frac{16}{15} }{2} = x}$

$\bf{\frac{16}{15} \times {\frac{1}{2}} = x}$

$\bf{\frac{8}{15} = x}$

Thus , The value of x is 8/15.

Now,
Let's verify

Substituting the value of x in the given equation.

8 / 15 + 2 / 3 = 3( 8 / 15 ) - 2 / 5

( 8 + 10 ) / 15 = ( 24 - 6 ) / 15

18 / 15 = 18 / 15

Thus,

Left Hand Side = Right Hand Side

Hence,
we can conclude that,

x = 8 / 15

Answer 2

hey mate! here's your answer!

x + $\frac{2}{3}$ = 3x - $\frac{2}{5}$

let us take the variable term one side and the fractional term other side, such that,

=> x - 3x = - $\frac{2}{5}$ - $\frac{2}{3}$

take LCM of the terms on right hand side!

=> -2x = $\frac{- 6 - 10}{15}$

=> x = $\frac{\cancel{-16}}{15}$ × $\frac{1}{\cancel{-2}}$

=> x = $\frac{8}{15}$

so, value of x is $\frac{8}{15}$.

VERIFICATION :-

Substitute the value of x in the equation!

=> $\frac{8}{15}$ + $\frac{2}{3}$ = $\cancel{3}$ × $\frac{8}{\cancel{15}}$ - $\frac{2}{5}$

take the LCM ,

=> $\frac{8 + 10}{15}$ = $\frac{8}{5}$ - $\frac{2}{5}$

=> $\frac{18}{15}$ = $\frac{8 - 2}{5}$

=> $\frac{6}{5}$ = $\frac{6}{5}$

THUS, R.H.S = L.H.S

$\bf{hence, proved!}$