|x|

<-- Enter Numerical Statement

Display the interval notation and set builder notation for |x|<3

Because we have an absolute value, we have two equations that we form:
The procedure for this is as follows for a variable x and a constant (c)
• x<(c)
• x>-(c)
Given this, we form our two equations:
• x<3
• x>-3
In interval notation, this is expressed as an or statement
Since we have an or statement, we break this up into two pieces
Piece 1 → x<3
Piece 2 → x>-3

Evaluate Piece 1
You entered the less than sign in the expression x<3
We start with the right side of the interval notation

Build the interval notation for x:
Since you did not enter an equal sign, this translates to ) since we will not be including the number 3
Based on the < you entered, the left side of the interval notation will extend to negative infinity, which is denoted as -∞

(-∞,3)

Set Builder Notation for x:
{ x | x<3 } where | denotes such that

Evaluate Piece 2
You entered the greater than sign in the expression x>-3
We start with the left side of the interval notation

Build the interval notation for x:
Since you did not enter an equal sign, this translates to ( since we will not be including the number -3
Based on the < you entered, the right side of the interval notation will extend to positive infinity, which is denoted as +∞

(-3,+∞)

Set Builder Notation for x:
{ x | x<3 } where | denotes such that

Now we take our two pieces and form our interval notation for x:
(-∞,3) U (-3,+∞)

Display the literal representation for x
-2,-1,0,1,2,3,4,5,6,7,...,∞