Question

find:-
a)4-(2y-3) = 3(y+2)+4
b) 4y+2/3y+7 = 2/3​

Answer 1

★ Solution (1) :-

$\sf \longrightarrow 4 - (2y - 3) = 3(y + 2) + 4$

$\sf \longrightarrow 4 - 2y + 3 = 3(y + 2) + 4$

$\sf \longrightarrow 4 - 2y + 3 = 3y + 6 + 4$

$\sf \longrightarrow 7 - 2y = 3y + 10$

$\sf \longrightarrow 7 - 10 = 3y + 2y$

$\sf \longrightarrow - 3 = 5y$

$\sf \longrightarrow y = \dfrac{ - 3}{5}$

★ Solution (2) :-

$\sf \longrightarrow \dfrac{4y + 2}{3y + 7} = \dfrac{2}{3}$

$\sf \longrightarrow 3(4y + 2) = 2(3y + 7)$

$\sf \longrightarrow 12y + 6 = 6y + 14$

$\sf \longrightarrow 12y - 6y = 14 - 6$

$\sf \longrightarrow 6y = 8$

$\sf \longrightarrow y = \dfrac{8}{6}$

$\sf \longrightarrow y = \dfrac{4}{3}$

Therefore, the answers are -3/5 and 4/3 respectively.

Answer 2

(a)

$\bf{4 - (2y - 3) = 3(y + 2) + 4}$

$\tt\implies{4 - 2y - ( - 3) = 3(y + 2) + 4}$

$\tt\implies{4 - 2y + 3 = 3(y + 2) + 4}$

$\tt\implies{7 - 2y = 3(y + 2) + 4}$

$\tt\implies{7 - 2y = 3y + 6 + 4}$

$\tt\implies{7 - 2y = 3y + 10}$

$\tt\implies{7 - 2y - 3y = 10}$

$\tt\implies{7 - 5y = 10}$

$\tt\implies{ - 5y = 10 - 7}$

$\tt\implies{ - 5y = 3}$

$\bf{ \large\implies} \: {{y = - \frac{3}{5}} = 0.6.}$

$\rule{200pt}{2pt}$

(b)

$\bf{\frac{4y+2}{3y+7}= \frac{2}{3} }$

Cross multiplying

$\tt \implies{3(4y+2)=2(3y+7)}$

$\sf\implies{12y+6=6y+14}$

$\sf\implies{12y+6-6y=14}$

$\sf\implies{6y+6=14}$

$\sf\implies{6y=14-6}$

$\sf\implies{6y=8}$

$\sf\implies{y=\cancel\frac{8}{6}}$

$\bf\implies{y=\frac{4}{3}}=1.33.$

$\rule{200pt}{4pt}$