Question

7y-5/4y+2 = 8/7 verify also

Answer 1

Given :

• $\sf \dfrac{7y - 5}{4y + 2} = \dfrac{8}{7}$

⠀ ⠀

To Find :

• Value of y = ?

⠀ ⠀

Solution :

⠀ ⠀

We are given :

$\sf \dfrac{7y - 5}{4y + 2} = \dfrac{8}{7}$

⠀ ⠀

To solve it, first we have to covert it in simple equation by cross multiplication method.

⠀ ⠀

By cross multiplication, we have :

$\sf : \implies (7y - 5) \times 7 = 8 \times (4y + 2)$

$\sf : \implies 49y - 35 = 32y + 16$

$\sf : \implies 49y - 35 - 32y - 16 = 0$

$\sf : \implies 17y - 51 = 0$

$\sf : \implies 17y = 51$

$\sf : \implies y = \dfrac{51}{17}$

$\sf : \implies y = \cancel{\dfrac{51}{17}}$

$\sf : \implies y = 3$

$\Large \underline{\boxed{\bf{y = 3}}}$

⠀ ⠀

Hence, value of y = 3.

⠀ ⠀

Verification :

⠀ ⠀

LHS = $\sf \dfrac{7y - 5}{4y + 2}$

Put value of y = 3 in equation :

$\sf : \implies \underline{\underline{\bf LHS}} = \dfrac{7(3) - 5}{4(3) + 2}$

$\sf : \implies \underline{\underline{\bf LHS}} = \dfrac{21 - 5}{12 + 2}$

$\sf : \implies \underline{\underline{\bf LHS}} = \dfrac{16}{14}$

$\sf : \implies \underline{\underline{\bf LHS}} = \cancel{\dfrac{16}{14}}$

$\sf : \implies \underline{\underline{\bf LHS}} = \dfrac{8}{7}$

⠀ ⠀

RHS = $\sf \dfrac{8}{7}$

⠀ ⠀

As, LHS = RHS,

Hence, Verified.

Answer 2

Step-by-step explanation:

$\large{\frac{7y - 5}{4y + 2}}\huge{⤱} {\frac{8}{7}}$

Cross multiply, we get ,

$7 ( \: 7y \: - 5 ) \: = \: 8(4y \: + \: 2)$

$49y \: - \: 35 \: = \: 32y \: + 16$

$49y - 32y = 16 + 35$

$17y = 51$

$y \: = \: \frac{51}{17} \\ = \: 3$

Verification : For y = 3

$= \frac{7y - 5}{4y + 2} \\ = \frac{7 \times 3 - 5}{4 \times 3 + 2}$

$= \: \frac{21 - 5}{12 + 2}$

$= \frac{16}{14}$

$= \frac{8}{7} = \bold{rhs}$