Question

please solve this question​

Answer 1

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

Method 1 :

By taking LCM for the LHS (Left hand side),

$\dfrac{(x - 3) + 4(2)}{2} = \dfrac{3x + 7}{4}$

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

By adding the constants in the LHS (Left hand side)

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

By cross multiplication,

$4(x + 5) = 2(3x + 7)$

$4x + 20 = 6x + 14$

Bringing all the constants to one side and variables to the other,

$20 - 14 = 6x - 4x$

$6 = 2x$

$\dfrac{ \not6}{ \not2} = x$

$3 = x$

Verification :-

By substituting x for 3,

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

$\dfrac{3 - 3}{2} + 4 = \dfrac{3(3) + 7}{4}$

$\dfrac{0}{2} + 4 = \dfrac{9 + 7}{4}$

$4 = \dfrac{16}{4}$

LHS = RHS

Hence verified