Question

How do you solve for $y:2x-4y<12?$

Answer 1

Hint: For these kinds of questions, all we have to do is make use of basic mathematics. We have to group all the like variable terms together and all the constant together. And then we have to make the variable what we want as the subject of the entire expression. So we have to convert the expression in a function where the variable we want stands as the main subject.

Complete step by step answer:
Let us consider, we have, $s=ax+b$ and we want to find $x$ from this equation. We have $s=ax+b$ . We will transfer my $b$ and $a$ to the other side which has $s$ . We get the following :
$\Rightarrow \dfrac{s-b}{a}=x$ . Now this became a function of $x$ and we got our $x$ .
And in the same way , we have to make this a function of $y$ .
Let’s bring $12$ from the left hand side of the in-equality to the right hand side. Upon doing so, we get the following :$$ $$
$\begin{align}
  & \Rightarrow 2x-4y<12 \\
 & \Rightarrow 2x-4y-12<0 \\
\end{align}$
Now let’s bring $4y$ onto the left hand side of the inequality from the right hand side. Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 2x-4y-12<0 \\
 & \Rightarrow 2x-12<4y \\
\end{align}$
Now let’s divide the entire equation by 4.The inequality symbol doesn’t change as we are diving it with a positive real number. Upon doing so , we get the following :
\[\Rightarrow \dfrac{x}{4}-3 < y\]
We can’t truly find the value of $y$ as we have two unknown i.e $x,y$ but only one equation. So we can’t ultimately find the value of $y$ or $x$. But what we can do here is to write one unknown with the help of others.

$\therefore $ Hence , upon solving for $y:2x-4y<12$ we get $y>\dfrac{x}{4}-3$.

Note: Please do not get confused upon seeing the inequality symbol. The mathematics behind is almost the same as the mathematics behind =. But the inequality symbol changes when we either multiply or divide the entire with a negative real number. And when we have two unknown variables , we must need two equations to completely solve for them and find an answer.