Question

How do you solve 12(5+2y)=4y-(6-9y)?

Answer 1

Hint: In this type of question, we will first expand the terms in the parenthesis on the right side as well as the left side of the equation by multiplying each term within the parenthesis with the term outside the parentheses. As we know that the linear equation with single variable y is in the form of y=C. So, we will make the equation in the form of y=C. After that, we will get the solution.

Complete step-by-step solution:
Let us solve this question.
We have to solve 12(5+2y)=4y-(6-9y).
First, we will expand the term which is given in the parenthesis.
After expanding the terms of the left side of equation, we get
\[\Rightarrow \]12(5)+12(2y)=4y-(6-9y)
Now, we will expand the terms of the right side of the equation.
\[\Rightarrow \]12(5)+12(2y)=4y-(6)-(-9y)
Now, we will multiply each of the terms which is inside the parenthesis with the term outside the parentheses. We get,
\[\Rightarrow \]60+24y=4y-6+9y
As we have known that the form of a linear equation with a single variable is y=C, where C is constant.
So, we will take all the terms of y in the left side of the equation and all the constants to the right side of the equation.
So, balancing the equation in that way, we get
\[\Rightarrow \]24y-4y-9y=-6-60
We can write the above equation as
\[\Rightarrow \]11y=-66
We can write the above equation as
\[\Rightarrow y=\dfrac{-66}{11}=-6\]
Hence, we get the value of y=-6.

Note: In case, if we want to satisfy ourselves that we have got the correct solution. Then, we can cross check our answer. We have a method to do that. We will just put the value of y in the given equation. After that, we will check if the right hand side of the equation and the left hand side of the equation are equal. If they are equal, then we will be satisfied that our solution was correct.
So, let us cross check by putting the value of y in the given equation.
12(5+2y)=4y-(6-9y)
By putting the value of y=-6 in the above equation, we get
\[\Rightarrow \]12(5+2(-6))=4(-6)-(6-9(-6))
We can the above equation as
\[\Rightarrow \]12(5-12)=-24-(6+54)
\[\Rightarrow \]12(-7)=-24-60
\[\Rightarrow \]-84=-84
Hence, we can see that the left hand side and right hand side of the equation are equal. So, the value of y as we have found that is -6 is correct.