Question

Solve: 4(y+3)/8 =7+ 5y/13​

Answer 1

Answer:

The solution of the given equation is $\displaystyle{\sf\:y\:=\:-\:\dfrac{25}{3}}$.

Step-by-step-explanation:

The given equation is $\displaystyle{\sf\:\dfrac{4\:(\:y\:+\:3\:)}{8}\:=\:\dfrac{7\:+\:5y}{13}}$

We have to find the solution of the equation.

Now,

$\displaystyle{\sf\:\dfrac{4\:(\:y\:+\:3\:)}{8}\:=\:\dfrac{7\:+\:5y}{13}}$

$\displaystyle{\implies\sf\:\dfrac{4y\:+\:12}{8}\:=\:\dfrac{7\:+\:5y}{13}}$

$\displaystyle{\implies\sf\:13\:\times\:(\:4y\:+\:12\:)\:=\:8\:\times\:(\:7\:+\:5y\:)}$

$\displaystyle{\implies\sf\:52y\:+\:156\:=\:56\:+\:40y}$

$\displaystyle{\implies\sf\:52y\:-\:40y\:=\:56\:-\:156}$

$\displaystyle{\implies\sf\:12y\:=\:-\:100}$

$\displaystyle{\implies\sf\:y\:=\:-\:\cancel{\dfrac{100}{12}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:y\:=\:-\:\dfrac{25}{3}}}}}$

∴ The solution of the given equation is $\displaystyle{\sf\:y\:=\:-\:\dfrac{25}{3}}$.

Answer 2

Answer:

Given :-

⇒ $\sf\dfrac{4(y + 3)}{8} =\: \dfrac{7 + 5y}{13}$

To Find :-

• What is the value of y.

Solution :-

$\mapsto$ $\sf\dfrac{4(y+ 3)}{8} =\: \dfrac{7 + 5y}{13}$

⇒ $\sf\dfrac{4y + 12}{8} =\: \dfrac{7 + 5y}{13}$

By doing cross multiplication we get,

⇒ $\sf 13(4y + 12) =\: 8(7 + 5y)$

⇒ $\sf 52y + 156 =\: 56 + 40y$

⇒ $\sf 52y - 40y =\: 56 - 156$

⇒ $\sf 12y =\: - 100$

⇒ $\sf y =\: \dfrac{\cancel{- 100}}{\cancel{12}}$

➠ $\sf y =\: \dfrac{- 25}{3}$

$\therefore$ The value of y is $\boxed{\bold{\large{\dfrac{- 25}{3}}}}$ .