Question

solve the equation and check the answer.​

Answer 1

Question :-

Solve $\sf \dfrac{4x + 1}{x + 4} = 5$

Answer :-

x = - 19

Solution :-

$\sf \dfrac{4x + 1}{x + 4} = 5$

$\sf \dfrac{4x + 1}{x + 4} = \dfrac{5}{1}$

By cross multiplication :-

⇒ (4x + 1)1 = 5(x + 4)

⇒ 4x + 1 = 5x + 20

Transpose 4x to RHS

⇒ 1 = 5x + 20 - 4x

⇒ 1 = x + 20

Transpose 20 to LHS

⇒ 1 - 20 = x

⇒ - 19 = x

⇒ x = - 19

Verification :-

$\sf \dfrac{4( - 19) + 1}{ - 19 + 4} = 5$

$\sf \dfrac{ - 76+ 1}{ - 19 + 4} = 5$

$\sf \dfrac{ - 75}{ - 15} = 5$

$\sf \dfrac{75}{15} = 5$

$\sf 5 = 5$

Answer 2

Answer:-

$\bold{ \frac{4x + 1}{x + 4} = 5}$

$\bold{ \frac{4x + 1}{x + 4} = \frac{5}{1} }$

[ cross multiplication ]

$\bold{1(4x + 1) = 5(x + 4)}$

$\bold{4x + 1 = 5x + 20}$

$\bold{4x - 5x = 20 - 1}$

$\bold{ - x = 19}$

$\boxed {x = - 19}$

Verification:-

[substitute x=-19 in place of x]

$\bold{ \frac{4( - 19) + 1}{ - 19 + 4} = \frac{5}{1} }$

$\bold{ \frac{ - 76 + 1}{ - 15} = \frac{5}{1} }$

$\bold{ \frac{ - 75}{ - 15} = \frac{5}{1} }$

$\bold{ \frac{5}{1} = \frac{5}{1} }$

Hence proved !