Question

How do you solve `8- 5y > - 37`?

Answer 1

`y < 9`

Explanation:

`8 - 5y > -37`

Solving inequalities is very similar to solving equations.

First, add `color(blue)(-37)` to both sides of the inequality:
`8 - 5y quadcolor(blue)(+quad37) > -37 quadcolor(blue)(+quad37)`

`45 - 5y > 0`

Add `color(blue)(5y)` to both sides of the inequality:
`45 - 5y quadcolor(blue)(+quad5y) > 0 quadcolor(blue)(+quad5y)`

`45 > 5y`

Now divide both sides by `color(blue)(5)`:
`45/color(blue)5 > (5y)/color(blue)5`

`9 > y`

However, we want our variable `y` to be on the left hand side while making `y` still be less than `9`, so it is:
`y < 9`

Hope this helps!