How do you solve for x in y=5x+9?

Sep 30, 2015

$x = \frac{y - 9}{5}$

Explanation:

In these problems, we want to get $x$ all by itself on one side of the equation and everything else on the other side. That's when we can say we've solved for $x$. So, we'll start by moving the 9 to the left side of the equation by subtracting it from both sides:

$y = 5 x + 9$
$y - 9 = 5 x + 9 - 9$

We can see that they cancel out, since $9 - 9 = 0$:

$y - 9 = 5 x \cancel{+ 9 - 9}$

Now, all we have to do to get $x$ by itself is to get rid of the 5 next to it. We do this by dividing by 5:

$y - 9 = 5 x$
$\frac{y - 9}{5} = \frac{5 x}{5}$

Because $\frac{5}{5} = 1$, the fives cancel:

$\frac{y - 9}{5} = \cancel{\frac{5}{5}} x$

To finish, we state our solution:

$x = \frac{y - 9}{5}$