The general rule is that if |x| < k, for some positive number k, then we can break that down into the compound inequality -k < x < k
In this case, k = 3 so if |x| < 3 then -3 < x < 3
To graph -3 < x < 3, we do the following:
Step 1) Draw out a number line. Make sure that key values -3 and 3 are present (along with others such as 0)
Step 2) Place open circles or holes at -3 and 3 on the graph.
Step 3) Shade between the two open circles
Following those steps and you'll get what you see attached, which is the first graph you posted (first on the left)
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Side Note: Saying |x| < 3 means that the distance x is from zero, |x|, is less than 3 units. So anything within a 3 unit radius, so to speak, of 0 will be the solution set. We are NOT including the endpoints -3 or 3. This is shown through the use of open circles. They are gaps in the solution set.
If you want the answer in interval notation, then you would write (-3,3)
Which unfortunately looks identical to ordered pair notation, but its not. Instead it means we have an interval from -3 to 3. The parenthesis tell us to exclude the endpoints.
