Question

How do you solve and graph `y - 2 > -3`?

Answer 1

`y > -1`
`color(white)("XXXX")`(see below for graphs)

Explanation:

Given an inequality, the following operations can be performed to both sides of the inequality without effecting the inequality relation:

1. Add any amount
2. Subtract any amount
3. Multiply by any amount `> 0`
4. Divided by any amount `> 0`

Given `y - 2 > -3`
We can add `2` to both sides, to get:
`color(white)("XXXX")` `y > -1`

Since this is a relationship involving a single variable, it could be graphed on a number line (top image below); notice the hollow circle which indicates that the value `(-1)` is not included in the solution set.

You could also graph this relationship on the Cartesian plane (bottom image below); again, notice the broken line on the left indicates that `(-1)` is not to be included in the solution set.