Question

Solve $\dfrac{{7y + 4}}{{y + 2}} = \dfrac{{ - 4}}{3}$
$A)\dfrac{{ - 4}}{5}$
$B)\dfrac{3}{2}$
$C)\dfrac{{ - 9}}{4}$
$D)\dfrac{1}{4}$

Answer 1

Hint: The addition is the sum of given two or more than two numbers, or variables and in addition, if we sum the two or more numbers then we obtain a new frame of the number will be found, also in subtraction which is the minus of given two or more than two numbers, but here comes with the condition that in subtraction the greater number sign represented in the number will stay constant example $2 - 3 = - 1$

Complete step by step answer:
Since given that $\dfrac{{7y + 4}}{{y + 2}} = \dfrac{{ - 4}}{3}$ and we asked to find the value of the unknown variable $y$
By the cross multiplication, we have $\dfrac{{7y + 4}}{{y + 2}} = \dfrac{{ - 4}}{3} \Rightarrow (7y + 4)3 = - 4(y + 2)$ the right-side denominator goes to the multiplication of the left side numerator and the left side denominator goes to the right side numerator
By the multiplication operation we have $21y + 12 = - 4y - 8$ (be careful at the negative multiplication)
Now making the variables on the left side and the numbers on the right side, then we have $21y + 12 = - 4y - 8 \Rightarrow 21y + 4y = - 8 - 12$
By the addition and subtraction operation, we get $25y = - 20$
Hence by the division, we have $y = \dfrac{{ - 20}}{{25}} \Rightarrow \dfrac{{ - 4}}{5}$ by the common terms of $5$. Hence we got the unknown variable as $y = \dfrac{{ - 4}}{5}$

So, the correct answer is “Option A”.

Note:
The other two operations which we used to solve the problem are multiplication and division operations.
Since multiplicand refers to the number multiplied. Also, a multiplier refers to multiplying the first number. Have a look at an example; while multiplying $5 \times 7$ the number $5$ is called the multiplicand and the number $7$ is called the multiplier.
The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $y = - \dfrac{{33}}{{11}} \Rightarrow - 3$