# SAT Math Practice: Solving for a Variable!

Today I’ll show you a problem I see a lot of students facing: how to solve for a variable if it appears in both the numerator and the denominator. Given the New SAT’s increased focus on simplifying equations, make sure you have this process down pat!

Given the equation $y=\dfrac{3x+5}{2x-8}$, give x in terms of y.

What this question is essentially wanting us to do is to isolate x on one side, so let’s get started! These steps will just about always carry you through problems like this, so pay close attention!

1) Move your denominator over to the left

$y(2x-8)=3x+5$

2) Distribute your second variable (i.e. y).

$2xy-8y=3x+5$

3) Move all your terms containing x to the left, and move all other terms to the right

$2xy-3x=8y+5$

4) Factor out your x term

$x(2y-3)=8y+5$

5) Move the parenthesis (i.e. not your x term) over to the right

$x=\dfrac{8y+5}{2y-3}$

And there you have it! We solved for a variable that appeared in both the numerator and the denominator! This question comes up pretty frequently, so again, make sure you’re comfortable with these steps, and make sure to practice!

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