# How do you solve 2y-9>5y+12?

Dec 21, 2016

$y < - 7$

#### Explanation:

First, isolate the $y$ term on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced:

$2 y - 9 - \textcolor{red}{2 y - 12} > 5 y + 12 - 9 - \textcolor{red}{2 y - 12}$

$2 y - 2 y - 9 - 12 > 5 y - 2 y + 12 - 12$

$0 - 9 - 12 > 5 y - 2 y + 0$

$- 9 - 12 > 5 y - 2 y$

Now we can group the like terms:

$- 21 > \left(5 - 2\right) y$

$- 21 > 3 y$

And lastly, we can solve for $y$ while keeping the inequality balanced:

(-21)/color(red)(3) > (3y)/(color(red)(3)

$- 7 > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} y}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}$

$- 7 > y$

And to get this solution in terms of $y$ we can reverse or "flip" the inequality:

$y < - 7$