Write the following intervals in the set-builder form
[-20,3)

Answer

To express the interval \([-20, 3)\) in set-builder notation, we follow these steps:

### Step 1: Identify the endpoints of the interval
The interval given is \([-20, 3)\). Here, \(-20\) is the lower limit and \(3\) is the upper limit.

### Step 2: Determine the type of interval
The square bracket \([-20\) indicates that \(-20\) is included in the interval (closed interval), while the parenthesis \(3)\) indicates that \(3\) is not included in the interval (open interval).

### Step 3: Write the conditions for the set-builder notation
In set-builder notation, we express the elements \(x\) that satisfy the conditions based on the endpoints:
- Since \(-20\) is included, we write \(x \geq -20\).
- Since \(3\) is not included, we write \(x < 3\).

### Step 4: Combine the conditions
We can now combine these conditions into a single statement in set-builder notation.

### Final Set-Builder Notation
The set-builder form for the interval \([-20, 3)\) is:
\[ \{ x \mid -20 \leq x < 3 \} \]