Step by step
The question
Question: solve |x| ≥ 2.
|x| ≥ 2
1 Draw the distance
2 Write it without bars
So x ≤ −2 or x ≥ 2.
x ≤ −2 or x ≥ 2
"Or" means: x can make one of them true, or the other.
We solve both, side by side.
or: one of them is true
So x ≤ −2 or x ≥ 2.
3 Show it on a number line
Books also write the answer like this.
It is called interval notation.
A square bracket means the end is in, like the filled circle.
∞ means it goes on for ever.
∪ means or.
interval: (−∞, −2] ∪ [2, ∞)
4 Check
Let's test one number from each part, in the question.
First −3.
x = −3: |−3| = 3
3 is greater than or equal to 2.
True!
3 ≥ 2
Now 3, from the right part.
x = 3: |3| = 3
3 is greater than or equal to 2.
True!
Both parts work!
3 ≥ 2
Let's look back.
First: draw the distance.
Then: write it without bars.
Then: show it on a number line.
Last: check.
Answer
or: one of them is true