Convert to Interval Notation x< -4 and x< 4

Solution:

Step 1: Determine the common elements between the two sets

Identify the numbers that satisfy both conditions $x < -4$ and $x < 4$.

Step 2: Express the solution using interval notation

Translate the inequality into interval notation. The solution is $\left(-\infty, -4\right)$.

Step 3: There is no third step as the solution is complete after step 2.

Knowledge Notes:

Interval notation is a way of writing subsets of the real number line. An interval notation consists of a pair of numbers that define the endpoints of the interval, along with parentheses or brackets to indicate whether the endpoints are included or excluded. Here are some key points to remember:

1. A parenthesis, "(", or ")", indicates that the endpoint is not included in the interval, also known as an open interval.

2. A bracket, "[", or "]", indicates that the endpoint is included in the interval, also known as a closed interval.

3. $-\infty$ and $\infty$ are not real numbers but are used to denote that the interval extends indefinitely in the negative or positive direction, respectively. They are always accompanied by parentheses since infinity cannot be included in the interval.

4. The intersection of two sets includes all elements that are common to both sets. In the context of inequalities, it refers to the set of numbers that satisfy both conditions.

In the given problem, we are looking for numbers that are less than -4 and also less than 4. Since all numbers less than -4 are also less than 4, the intersection of these two conditions is simply the set of numbers less than -4. This is why the interval notation for the solution is $\left(-\infty, -4\right)$, indicating all numbers from negative infinity up to, but not including, -4.