How to write an interval union in inequality form

Q: How do you read [-4,1] union [9,infinity) in inequalities?

It means -4 = 9. The word union corresponds to or.

Q: Why is x >= -4 not correct here?

Because that would include values like 5 and 7, which are not in the interval [-4,1] or the interval [9, infinity).

Question

50.
[-4,1]\cup[9,\infty)

=-1? x\ge -4 	ext{ or } x\ge 9.

Acemy AI · Accepted Answer

**Key takeaway**: This kind of question is really about reading interval notation carefully. The endpoints matter, and the word “or” is usually the bridge between the pieces.

The set

$$[-4,1]\cup[9,\infty)$$

means all real numbers that satisfy **either** of these conditions:

- $-4\le x\le 1$
- $x\ge 9$

So the inequality form is

$$-4\le x\le 1 \quad 	ext{or} \quad x\ge 9.$$

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**Pitfalls the pros know** 👇
Do not turn the union into a single inequality like $x\ge -4$ or $x\ge 9$; that would include numbers such as 5, which are not in the set. Also, the bracket in $[-4,1]$ means the endpoints are included.

**What if the problem changes?**
If the union were $(-4,1]\cup[9,\infty)$, then the first part would change to $-4<x\le 1$. If it were $[-4,1]\cap[9,\infty)$, the answer would be empty because the two intervals do not overlap.

`Tags`: interval notation, union of sets, inequality form

Question

How to write an interval union in inequality form

Expert Verified Solution

FAQ

How do you read [-4,1] union [9,infinity) in inequalities?

Why is x >= -4 not correct here?