Question

7y+4/y+2 equals to -4/3​

Answer 1

Answer:

$\large{\underline{\boxed{\sf -\dfrac{4}{5}}}}$

Step-by-step explanation:

Given that ;

$\sf \frac{7y + 4}{y + 2} = - \frac{4}{3} \\ \\ \bf on \: cross - multiplying : \\ \\ \implies \sf 3(7y + 4) = - 4(y + 2) \\ \\\implies \sf 21y + 12 = - 4y - 8 \\ \\ \implies \sf 21y + 4y = - 8 - 12 \\ \\ \implies \sf 25y = - 20 \\ \\ \implies \sf y = - \frac{20}{25} \\ \\ \boxed{ \bf \therefore \: y = - \frac{4}{5}}$

Verification;

Putting the value of y in above equation;

$\sf \frac{7y + 4}{y + 2} = - \frac{4}{3} \\ \\ \implies \sf \frac{7( - \frac{4}{5}) + 4}{( - \frac{4}{5} ) + 2} = - \frac{4}{3} \\ \\ \implies \sf \frac{ - \frac{28}{5} + 4}{ - \frac{4}{5} + 2 } = - \frac{4}{3} \\ \\ \implies \sf \frac{ \frac{- 28 + 20}{5} }{ \frac{ - 4 + 10}{5} } = - \frac{4}{3} \\ \\ \implies \sf \frac{ - \frac{8}{5} }{ \frac{6}{5} } = - \frac{4}{3} \\ \\ \implies \sf - \frac{8}{5} \times \frac{5}{6} = - \frac{4}{3} \\ \\ \implies \sf - \frac{4}{3} = - \frac{4}{3}$

∴ LHS = RHS

Hence, the answer is $\bf -\dfrac{4}{5}$.