Question

question of linear equation​

Answer 1

Answer:-

The Required value of x is 3.

Explanation:-

Given Equation:-

$\\ \bf\mapsto \: \dfrac{x - 3}{2} + 4 = \frac{3x + 7}{4} .$

To Find:-

• The Solution of the equation, that is the value of x.

Solution:-

$\\ \tt\mapsto \: \dfrac{x - 3}{2} + 4 = \frac{3x + 7}{4} .$

$\\ \tt\mapsto \dfrac{ x - 3 + 2(4)}{2} = \dfrac{3x + 7}{4} . \\ \\ \rm{ \bigg(by \: \: tak ing \: \: lcm. \bigg)}$

$\\ \tt\mapsto \frac{x - 3 + 8}{2} = \frac{3x + 7}{4} .$

$\\ \tt\mapsto \frac{x + 5}{2} = \frac{3x + 7}{4} .$

$\\ \tt\mapsto4 \bigg( \frac{x + 5}{2} \bigg) = 3x + 7 . \\ \\ \rm \: transporting \: \: 4 \: \: to \: \: LHS.$

$\\ \tt\mapsto4(x + 5) = 2(3x + 7) \: \: \: \\ \\ \rm transporting \: \: 2 \: \: to \: \: RHS.$

$\\ \tt\mapsto 4x + 20 = 6x + 14. \\ \\ \rm \: openi ng \: \: brackets.$

$\\ \tt\mapsto4x - 6x= 14 - 20.$

$\\ \tt\mapsto \cancel{ - } \: \: 2x = \cancel{ - } \: \: 6.$

$\\ \tt\mapsto2x = 6.$

$\\ \tt\mapsto x = \dfrac{6}{2} .$

$\\ \large\bf\mapsto \boxed{ \bf{x = 3.}}$

Therefore The Required Value Of x is 3.

Answer 2

$\large{\underline{\purple{\textbf{Given:-}}}}$

$\sf \quad \bullet Equation = \dfrac{x - 3}{2} + 4 = \dfrac{3x + 7}{4}$

$\large{\underline{\purple{\textbf{Find:-}}}}$

$\sf \quad \bullet value \: of \: x$

$\large{\underline{\purple{\textbf{Solution:-}}}}$

$\sf \dashrightarrow \dfrac{x - 3}{2} + 4 = \dfrac{3x + 7}{4}$

$\red\bigstar$ Taking L.C.M

$\sf \dashrightarrow \dfrac{x - 3 + 2 \times 4}{2}= \dfrac{3x + 7}{4}$

$\sf \dashrightarrow \dfrac{x - 3 + 8}{2}= \dfrac{3x + 7}{4}$

$\sf \dashrightarrow \dfrac{x + 5}{2}= \dfrac{3x + 7}{4}$

$\pink\bigstar$ Cross-multiplication

$\sf \dashrightarrow 4(x + 5) =2(3x + 7)$

$\sf \dashrightarrow 4x +20 =6x + 14$

$\purple\bigstar$ Collect like terms

$\sf \dashrightarrow 4x - 6x =14 - 20$

$\sf \dashrightarrow - 2x = - 6$

$\sf \dashrightarrow \not{-} 2x = \not{-} 6$

$\sf \dashrightarrow 2x =6$

$\sf \dashrightarrow x = \dfrac{6}{2}$

$\sf \dashrightarrow x = 3$

$\underline{\boxed{\sf\therefore Value\:of\:x\:will\:be\:3}}$