Question

Solve the equation $\dfrac{{5y - 4}}{8} - \dfrac{{(y - 3)}}{5} = \dfrac{{y + 6}}{4}$
$A)8$
$B)2$
$C)4$
$D)6$

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 and represented as $ + $ , 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 solution:
Since given that the equation $\dfrac{{5y - 4}}{8} - \dfrac{{(y - 3)}}{5} = \dfrac{{y + 6}}{4}$ and then we need to find the value of the unknown variable $y$, so we will make use of the basic mathematical operations to simplify further.
Starting with the cross multiplication on the both sides we get,
$\dfrac{{5y - 4}}{8} - \dfrac{{(y - 3)}}{5} = \dfrac{{y + 6}}{4} $
$\Rightarrow \dfrac{{5(5y - 4) - 8(y - 3)}}{{8 \times 5}} = \dfrac{{y + 6}}{4}$
Using the multiplication operation, we have,
$\dfrac{{25y - 20 - 8y + 24}}{{40}} = \dfrac{{y + 6}}{4}$
Canceling the common terms and again by the cross multiplication we get,
$\dfrac{{25y - 20 - 8y + 24}}{{10}} = y + 6$
$ \Rightarrow 25y - 20 - 8y + 24 = 10(y + 6)$
Hence, we have
$25y - 20 - 8y + 24 = 10y + 60$
now Turing the variables on the left-hand side and also the numbers on the right-hand side we get,
$25y - 20 - 8y + 24 = 10y + 60 $
$\Rightarrow 25y - 8y - 10y = 60 + 20 - 24$
while changing the values on the equals to, the sign of the values or the numbers will change.
By the addition and subtraction, we get,
$7y = 56$
Hence by the division operation we get,
 $y = \dfrac{{56}}{7}$
$ \Rightarrow y= 8$
Thus, $y = 8$ which is the unknown value of the given variable. Thus option $A)8$ is correct.

Note: The other two operations 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 $ - 4x \geqslant - 8 \Rightarrow 4x \leqslant 8 \Rightarrow $ the number $7$ is called the multiplier. Like $2 \times 3 = 6$ or which can be also expressed in the form of $2 + 2 + 2(3times)$
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 $y = \dfrac{{56}}{7} \Rightarrow 8$
Hence using simple operations, we solved the given problem.