Question

How do you solve `6x + 4y > 12`?

Answer 1

`" "`
`y>3-(3/2)x`

Explanation:

`" "`
We have the inequality `color(red)(6x+4y>12`

Subtract `color(blue)(6x` from both sides of the inequality

`6x+4y-color(blue)(6x)> 12 - color(blue)(6x`

`cancel(6x)+4y-color(blue)(cancel (6x))> 12 - color(blue)(6x`

`4y>12-6x`

We want just `color(red)(y` on the left-hand side of the inequality.

Divide both sides of the inequality by `color(red)(4`

`(4y)/color(red)(4) >(12-6x)/color(red)(4`

`(cancel 4/cancel color(red)(4))y>(cancel 12^color(red)(3)/color(red)(cancel 4^color(red)(1)))-(cancel 6^color(red)(3)/color(red)(cancel 4^color(red)(2)))x`

`y>3-(3/2)x`

We can verify this solution using an inequality graph:

The dotted line in the graph indicates the solution that is NOT the part of the solution.

Hope it helps.