# How do you solve for y in 9-y=1.5x?

Dec 29, 2015

$9 = 1.5 x + y$
$y = 9 - 1.5 x$

OR

$- y = 1.5 x - 9$
$- 1 \left(- y\right) = - 1 \left(1.5 x - 9\right)$
$y = 9 - 1.5 x$

#### Explanation:

There are two methods for rearranging this equation.

## Term Transaction

1. Add $y$ to both sides of the equation:
$9 = 1.5 x + y$
2. Subtract $1.5 x$ from both sides of the equation:
$9 - 1.5 x = y \text{ or } y = 9 - 1.5 x$

Notice that the variables have simply changed places and reversed their signs.

## Multiply through by $- 1$

1. Subtract 9 from both sides of the equation:
$- y = 1.5 x - 9$
2. Multiply both sides of the equation by $- 1$:
$- 1 \left(- y\right) = - 1 \left(1.5 x - 9\right)$
$y = - 1.5 x + 9 \text{ or } y = 9 - 1.5 x$