Question

solve x/2-1/5=x/3+1/5​

Answer 1

answer

18

$\frac{5x - 2}{10} = \frac{5x - 3}{15} \\ 15(5x - 2) = 10(5x + 30) \\ 65x - 30 = 50x + 300 \\ 65x - 50x = 300 - 30 \\ 15x = 270 \\ x = \frac{270}{15} \\ x = 18$

Answer 2

★ Solution :-

We have two methods to solve this question, we'll solve both of them.

The first method is as follows.

$\sf \leadsto \dfrac{x}{2} - \dfrac{1}{5} = \dfrac{x}{3} + \dfrac{1}{5}$

$\sf \leadsto \dfrac{5x - 2}{10} = \dfrac{5x + 3}{15}$

$\sf \leadsto 15(5x - 2) = 10(5x + 3)$

$\sf \leadsto 75x - 30 = 50x + 30$

$\sf \leadsto 75x - 50x = 30 + 30$

$\sf \leadsto 25x = 60$

$\sf \leadsto x = \dfrac{60}{25}$

$\sf \leadsto x = \dfrac{12}{5}$

$\:$

Now, we'll find the value of x by an other method.

$\sf \leadsto \dfrac{x}{2} - \dfrac{1}{5} = \dfrac{x}{3} + \dfrac{1}{5}$

$\sf \leadsto \dfrac{x}{2} - \dfrac{x}{3} = \dfrac{1}{5} + \dfrac{1}{5}$

$\sf \leadsto \dfrac{3x - 2x}{6} = \dfrac{1 + 1}{5}$

$\sf \leadsto \dfrac{1x}{6} = \dfrac{2}{5}$

$\sf \leadsto 5(1x) = 6(2)$

$\sf \leadsto 5x = 12$

$\sf \leadsto x = \dfrac{12}{5}$

Therefore, the value of x is $\sf \dfrac{12}{5}$

Now, let's check that, our answer is right or wrong.

$\sf \leadsto \dfrac{x}{2} - \dfrac{1}{5} = \dfrac{x}{3} + \dfrac{1}{5}$

$\sf \leadsto \dfrac{\dfrac{12}{5}}{2} - \dfrac{1}{5} = \dfrac{\dfrac{12}{5}}{3} + \dfrac{1}{5}$

$\sf \leadsto \bigg( \dfrac{12}{5} \times \dfrac{1}{2} \bigg) - \dfrac{1}{5} = \bigg( \dfrac{12}{5} \times \dfrac{1}{3} \bigg) + \dfrac{1}{5}$

$\sf \leadsto \dfrac{12}{10} - \dfrac{1}{5} = \dfrac{12}{15} + \dfrac{1}{5}$

$\sf \dashrightarrow \dfrac{12 - 2}{10} = \dfrac{12 + 3}{15}$

$\sf \dashrightarrow \dfrac{10}{10} = \dfrac{15}{15}$

$\sf \dashrightarrow 1 = 1$

Thus, we can conclude that the answer obtained is correct.