Question

Solve the equation and verify​

Answer 1

Question :

Solve the equation and verify :

• $\sf \dfrac{4x + 1}{3x - 2} = - 2$

Answer :

$\large \underline{\boxed{\bf x = 0.3}}$

Solution :

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

By cross multiply, we get :

$\sf : \implies 4x + 1 = - 2 \times (3x-2)$

$\sf : \implies 4x + 1 = - 6 x + 4$

$\sf : \implies 4x + 1 + 6 x - 4 = 0$

$\sf : \implies 10x - 3 = 0$

$\sf : \implies 10x = 3$

$\sf : \implies x = \dfrac{3}{10}$

$\sf : \implies x = 0.3$

$\large \underline{\boxed{\bf{x = 0.3}}}$

Verification :

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

$\bf \underline{\boxed{\bf LHS}} = \dfrac{4x + 1}{3x - 2}$

By substituting value of x = 0.3

$\sf : \implies LHS = \dfrac{4(0.3) + 1}{3(0.3) - 2}$

$\sf : \implies LHS = \dfrac{4 \times \dfrac{3}{10} + 1}{3 \times \dfrac{3}{10} - 2}$

$\sf : \implies LHS = \dfrac{\dfrac{12}{10} + \dfrac{10}{10}}{\dfrac{9}{10} - \dfrac{20}{10}}$

$\sf : \implies LHS = \dfrac{\dfrac{12+ 10}{10}}{\dfrac{9-20}{10}}$

$\sf : \implies LHS = \dfrac{\dfrac{22}{10}}{\dfrac{- 11}{10}}$

$\sf : \implies LHS = \dfrac{\cancel{22}}{\cancel{10}} \times \dfrac{\cancel{10}}{- \cancel{11}}$

$\sf : \implies LHS = \dfrac{2}{-1}$

$\sf : \implies LHS = - 2$

$\bf \underline{\boxed{\bf RHS}} = - 2$

$\underline{\boxed{\bf As, \: LHS = RHS.}}$

$\underline{\boxed{\bf Hence, \: verified}}$