Question

How do you solve and write the following in interval notation: `-2 ≤ x + 4` OR `-1 + 3x > -8`?

Answer 1

`[-6,\infty)`

Explanation:

You can rewrite `-2 \le x+4` as

`-2-4 \le x+4-4 \implies -6 \le x \implies x \ge -6`

Similarly, rewrite `-1+3x>-8` as

`-1+3x+1>-8+1 \implies 3x>-7 \implies x> -7/3`

Since `-6< -7/3`, any number which is greater than `-7/3` will automatically be greater than `-6`. And since the OR condition requires at least one of the conditions to be true, it is sufficient to ask `x \ge -6`

To write it in interval notation, we must find the boundaries of the desired region. We want `x` to be greater than `-6`, but we have no upper bound, which means it's `\infty`.

So, the interval is `[-6,\infty)`