How to isolate y?
I've got an equation: $$-4y=12-3x$$
I want to simply isolate the y variable so i could get rid of the -4 coefficient of the y variable.
What can I do to isolate the y variable? I've done the following but i'm not sure:
$$ y = \frac{12}{-4}-\frac{3x}{-4} $$
Is that the right way for solving this kind of equation? if not, what can i do?
Thanks in advance, really appreciate that.
3 Answers
$\begingroup$Yes.
$-4y = 12-3x$ will become $$y = -3 + (3/4)x$$
...after dividing both sides by $-4$
$\endgroup$ $\begingroup$Multiply both sides by $-\tfrac{1}{4}$, we have
\begin{align*} -\frac14 \times (-4y) &= -\frac14\times (12 -3x)\\ y &= -\frac14 \times 12 -\frac14 \times (-3x)\\ &= -3 + \tfrac34 x \end{align*}
$\endgroup$ $\begingroup$What you've done is correct. Basically, you want the $y$-term to be on one side and then divide: $$ -4y = 12-3x \implies 4y = 3x - 12 \implies y = \boxed {\dfrac {3x-12}{4} = \dfrac {3}{4}x - 3}. $$
$\endgroup$
