Question

solved the question​

Answer 1

Solution:-

Given :-

$\sf \implies \dfrac{2}{3} (4x - 1) - \bigg(2x - \dfrac{1 + x}{3} \bigg) = \dfrac{1}{3} x + \dfrac{4}{3}$

Now Take LCM

$\sf \implies \: \dfrac{2(4x - 1)}{3} - \bigg( \dfrac{6x - 1 - x}{ 3} \bigg) = \dfrac{x + 4}{3}$

$\sf \implies \: \dfrac{8x - 2}{3} - \dfrac{5x - 1}{3} = \dfrac{x + 4}{3}$

$\sf \implies \: \dfrac{8x - 2 - 5x + 1}{3} = \dfrac{x + 4}{ 3}$

$\sf \implies \: \dfrac{8x - 2 - 5x + 1}{ \cancel3} = \dfrac{x + 4}{ \cancel3}$

$\sf \implies \: 8x - 2 - 5x + 1 = x + 4$

$\sf \implies \: 3x - 1 = x + 4$

$\sf \implies \: 3x - x = 4 + 1$

$\sf\implies \: 2x = 5$

$\sf \implies \: \: x = \dfrac{5}{2}$

Answer is

$\sf \implies \: x = \dfrac{5}{2}$

Definition of Linear equation

=> A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.