Question

How do you solve and graph `(3x - 5) / 2 < 2x + 2`?

Answer 1

`x> -9`

Explanation:

Your goal here is to isolate `x` on one side of the inequality. Start by multiplying the right-hand side of the inequality by `1= 2/2`

`(3x-5)/2 < (2x+2) * 2/2`

This is equivalent to

`3x - 5 < 2(2x+2)`

`3x-5 < 4x + 4`

Now move `-5` and `4x` on the other sides of the inequality - don't forget to change their signs when you do that!

`3x - 4x < 4+ 5`

`-x < 9`

`x > -9`

This means that your inequality will be satisfied by any value of `x` that is bigger than `-9`. The solution set will be `x in (-9, + oo)`.

You can graph this by drawing a dashed vertical line at `x=-9`. Since you need the values of `x` that are bigger than `-9`, shade the area to the right of the dashed vertical line.

graph{x > -9 [-18.02, 18.03, -9.01, 9.01]}