Question

Solve the following equation. 2/5x - 5/2x = 1/10​

Answer 1

Answer:

Given:-

Solve the following equation : $\dfrac{2}{5}x - \dfrac{5}{2}x = \dfrac{1}{10}$.

To Find:-

The given equation.

Note:-

●》Here, we have to find the value of "x" by transposing the terms.

●》Transposing - For finding unknown value, we transposed known value and that signs are also changed ( signs are not change during transposing of multiple and divisional value ). For example - Multiple becomes Divisional.

●》Equation - It means two side term calculations should be equal i.e. L.H.S = R.H.S

Solution:-

$\huge\red{\dfrac{2}{5}x - \dfrac{5}{2}x = \dfrac{1}{10}}$

$\huge\red{Value \ \ of \ \ "x" = ?}$

☆ According to note first point and equation is~

▪︎$\dfrac{2}{5}x - \dfrac{5}{2}x = \dfrac{1}{10}$

☆ L.C.M = 10~

▪︎$\dfrac{2}{5}x × \dfrac{2}{2} - \dfrac{5}{2}x × \dfrac{5}{5} = \dfrac{1}{10}$

▪︎$\dfrac{4}{10}x - \dfrac{25}{10}x = \dfrac{1}{10}$

▪︎$- \ \dfrac{21}{10}x = \dfrac{1}{10}$

☆ According to note second point~

▪︎$x = \dfrac{1}{10} ÷ - \ \dfrac{21}{10}$

☆ Reciprocating the term~

▪︎$x = \dfrac{1}{10} × - \ \dfrac{10}{21}$

▪︎$x = - \ \dfrac{10}{210}$

☆ After reducing~

▪︎$x = - \ \dfrac{1}{21}$

$\huge\pink{x = - \ \dfrac{1}{21}}$

Checking:-

♤ Let's check accordingly to note third point~

• $\dfrac{2}{5}x - \dfrac{5}{2}x = \dfrac{1}{10} \implies ?$

♤ Applying "x" value~

• $\dfrac{2}{5} × - \ \dfrac{1}{21} - \dfrac{5}{2} × - \ \dfrac{1}{21} = \dfrac{1}{10} \implies ?$

♤ Minus × Minus = Plus~

• $- \ \dfrac{2}{105} + \dfrac{5}{42} = \dfrac{1}{10} \implies ?$

♤ L.C.M = 210~

• $- \ \dfrac{2}{105} × \dfrac{2}{2} + \dfrac{5}{42} × \dfrac{5}{5} = \dfrac{1}{10} \implies ?$

• $- \ \dfrac{4}{210} + \dfrac{25}{210} = \dfrac{1}{10} \implies ?$

• $\dfrac{25}{210} - \dfrac{4}{210} = \dfrac{1}{10} \implies ?$

• $\dfrac{21}{210} = \dfrac{1}{10} \implies ?$

• $\dfrac{1}{10} = \dfrac{1}{10} \implies ✔$

$\huge\green{Hence, Proved : x = - \ \dfrac{1}{21}}$

Answer:-

Hence, the value of "x" = $- \ \dfrac{1}{21}$.

:)