Question

$\frac{5x}{3} - \frac{x - 2}{4} = 2 \frac{1}{4} - ( x - \frac{2x - 1}{3} )$
find the value of x
answer aana chahiye
$\frac{17}{21}$
yani 17/21 answer aana chahiye
ekdam aasan tarike se solve karna
class 8 maths Manjit Singh
Linear equations in one variable

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Answer 1

Question:

• $\dfrac{5x}{3} -\dfrac{x-2}{4}=2\dfrac{1}{4}-\left(x-\dfrac{2x-1}{3}\right)$ . To find the value of x.

Solution:

$\dashrightarrow \dfrac{5x}{3} -\dfrac{x-2}{4}=2\dfrac{1}{4}-\left(x-\dfrac{2x-1}{3}\right)$

Simplifying by LCM :

$\dashrightarrow \dfrac{5x\times 4-(x-2)\times 3 }{12}=\dfrac{9}{4}-\left(\dfrac{x}{1}-\dfrac{2x-1}{3}\right)$

$\dashrightarrow \dfrac{20x - 3(x-2) }{12}=\dfrac{9}{4}-\left(\dfrac{3\times x -(2x-1)\times 1}{3}\right)$

$\dashrightarrow \dfrac{20x - 3x+6 }{12}=\dfrac{9}{4}-\left(\dfrac{3 x -(2x-1)}{3}\right)$

Adding like terms:

$\dashrightarrow \dfrac{17x+6 }{12}=\dfrac{9}{4}-\left(\dfrac{x+1}{3}\right)$

Transporting (x+1)/3 from R.H.S to L.H.S {sign will be change}

$\dashrightarrow \dfrac{17x+6 }{12}+\left(\dfrac{x+1}{3}\right)=\dfrac{9}{4}$

$\dashrightarrow \dfrac{(17x+6)\times 1+(x+1)\times 4}{12}=\dfrac{9}{4}$

Taking LCM:

$\dashrightarrow \dfrac{(17x+6)+(4x+4)}{12}=\dfrac{9}{4}$

Adding like terms :

$\dashrightarrow \dfrac{21x+10}{12}=\dfrac{9}{4}$

Cross-Multiplying:

$\dashrightarrow (21x+10)4 = 9\times 12$

$\dashrightarrow 84x+40= 108$

Transporting 40 from L.H.S to R.H.S :

$\dashrightarrow 84x= 68$

$\dashrightarrow x = \cancel{\dfrac{68}{82}}\\\\\dashrightarrow x=\dfrac{17}{21}$

Therefore,

• value of x is 17/21