Question

How do you graph the inequality `x - 1 > -10` on a number line?

Answer 1

With an open dot at the `-9` position and extending to the right.

In inequalities you are allowed to add or subtract the same number at both sides.

You are also allowed to multiply both sides with the same number,
BUT : if the number you multiply by is negative, the inequality reverses:
`>` becomes `<` and vice versa.

In this case we only have to add `1` to both sides:
`x-1> -10->x> -9`

The `>` means the graph extends to the right
(that's where the `>` is pointing to!)

Since the value of `x=-9` is not included, you draw an "open" dot at the `-9` position.
In some methods an open half circle is used.

(If it were `x>=-9` you'd draw a closed and filled dot)