Question

The sum of three rational numbers -2/3, x and ¾ is ¼ , find the value of x​

Answer 1

Answer:

1/6

Explanation:

As per the provided information in the given question, we have :

• Sum of three rational numbers -2/3, x and ¾ is ¼.

We are asker to calculate the value of x.

According to the question,

$\longmapsto \rm {\dfrac{-2}{3} + x + \dfrac{3}{4} = \dfrac{1}{4} }$

Taking the L.C.M and making the denominator same in L.H.S.

$\longmapsto \rm {\dfrac{-8 + 12x + 9}{12} = \dfrac{1}{4} }$

Rearranging the terms in the numerator of L.H.S.

$\longmapsto \rm {\dfrac{12x + 9-8}{12} = \dfrac{1}{4} }$

Performing subtraction.

$\longmapsto \rm {\dfrac{12x + 1 }{12} = \dfrac{1}{4} }$

Now, by cross multiplication, we have :

$\longmapsto \rm {4(12x + 1 ) = 1(12) }$

Performing multiplication.

$\longmapsto \rm {48x + 4 = 12}$

Transposing 4 from L.H.S to R.H.S. Its arithmetic operator will get changed.

$\longmapsto \rm {48x = 12 - 4}$

Performing subtraction in R.H.S.

$\longmapsto \rm {48x = 8}$

Transposing 48 from L.H.S to R.H.S. Its arithmetic operator will get changed.

$\longmapsto \rm {x =\cancel{ \dfrac{8}{48}} }$

Dividing the numerator and the denominator in R.H.S by 8.

$\longmapsto \bf {x = \dfrac{1}{6} }$

∴ Value of x is 1/6.

$\rule{200}2$

⠀⠀⠀⠀⠀Transposition Method

• This is the method used to solve a linear equation having variables and constants.

• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.